Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de 1/(x+3)
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Derivada de 4*y
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Derivada de (-1)/x-3*x
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Derivada de y=csc(3x²+1)
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Expresiones idénticas
- y=ln(absolute(cos(x^(uno / dos))))+x^(uno / dos)*tg(x^(uno / dos))
- y es igual a ln(absolute( coseno de (x en el grado (1 dividir por 2)))) más x en el grado (1 dividir por 2) multiplicar por tg(x en el grado (1 dividir por 2))
- y es igual a ln(absolute( coseno de (x en el grado (uno dividir por dos)))) más x en el grado (uno dividir por dos) multiplicar por tg(x en el grado (uno dividir por dos))
- y=ln(absolute(cos(x(1/2))))+x(1/2)*tg(x(1/2))
- y=lnabsolutecosx1/2+x1/2*tgx1/2
- y=ln(absolute(cos(x^(1/2))))+x^(1/2)tg(x^(1/2))
- y=ln(absolute(cos(x(1/2))))+x(1/2)tg(x(1/2))
- y=lnabsolutecosx1/2+x1/2tgx1/2
- y=lnabsolutecosx^1/2+x^1/2tgx^1/2
- y=ln(absolute(cos(x^(1 dividir por 2))))+x^(1 dividir por 2)*tg(x^(1 dividir por 2))
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Expresiones semejantes
- y=ln(absolute(cos(x^(1/2))))-x^(1/2)*tg(x^(1/2))
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Expresiones con funciones
- ln
- ln(x+10)^11
- ln((x^2)-1)
- ln3x^5
- ln^3(x^2+1)
- ln(1+|x|)
- Coseno cos
- cos(log(x))+x^2*tan(x)
- cos(-6x+7)
- cos(3*x)/3
- cos(2*x+pi/3)
- cos(2-3*x)
Derivada de y=ln(absolute(cos(x^(1/2))))+x^(1/2)*tg(x^(1/2))
Solución
Ha introducido
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/| / ___\|\ ___ / ___\ log\|cos\\/ x /|/ + \/ x *tan\\/ x /
$$\sqrt{x} \tan{\left(\sqrt{x} \right)} + \log{\left(\left|{\cos{\left(\sqrt{x} \right)}}\right| \right)}$$
log(Abs(cos(sqrt(x)))) + sqrt(x)*tan(sqrt(x))
Primera derivada
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// / _________ \ / _________ \ / _________ \ / _________ \\ / / _________ \ / _________ \ / _________ \ / _________ \\ \
|| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\|| | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| |
||cos| / ------- *cos|-----------||*sign(x)*sin|-----------|*sinh| / ------- *sin|-----------|| cos|-----------|*cosh| / ------- *sin|-----------||*sign(x)*sin| / ------- *cos|-----------||| / _________ \ / _________ \ | cos|-----------|*cos| / ------- *cos|-----------||*sign(x)*sinh| / ------- *sin|-----------|| cosh| / ------- *sin|-----------||*sign(x)*sin|-----------|*sin| / ------- *cos|-----------||| / _________ \ / _________ \|
|| \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 //| | / x /atan2(0, x)\| | / x /atan2(0, x)\| | \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 //| | / x /atan2(0, x)\| | / x /atan2(0, x)\|| / / ___\\
||------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------|*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------|| - |- ------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------|*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|||*sign\cos\\/ x //
|| _________ _________ | \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // | _________ _________ | \\/ sign(x) \ 2 // \\/ sign(x) \ 2 //|
|| / x / x | | / x / x | |
2/ ___\ / ___\ || 2* / ------- 2* / ------- | | 2* / ------- 2* / ------- | |
1 tan \\/ x / tan\\/ x / \\ \/ sign(x) \/ sign(x) / \ \/ sign(x) \/ sign(x) / /
- + ----------- + ---------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 ___ | / ___\| / ___\
2*\/ x |cos\\/ x /|*cos\\/ x /
$$\frac{\left(- \left(- \frac{\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{2 \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} - \frac{\cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{2 \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}}\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} + \left(- \frac{\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{2 \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} + \frac{\sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{2 \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}}\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \operatorname{sign}{\left(\cos{\left(\sqrt{x} \right)} \right)}}{\cos{\left(\sqrt{x} \right)} \left|{\cos{\left(\sqrt{x} \right)}}\right|} + \frac{\tan^{2}{\left(\sqrt{x} \right)}}{2} + \frac{1}{2} + \frac{\tan{\left(\sqrt{x} \right)}}{2 \sqrt{x}}$$
Segunda derivada
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/ / / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \\ / / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ / _________ \ \ / / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \ / / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \ / / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \ / / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \\
| | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\| 2/atan2(0, x)\ / 2*x*DiracDelta(x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| 2/atan2(0, x)\ / 2*x*DiracDelta(x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ /atan2(0, x)\ /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\|| | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\| 2/atan2(0, x)\ / 2*x*DiracDelta(x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| 2/atan2(0, x)\ / 2*x*DiracDelta(x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\| / 2*x*DiracDelta(x)\ | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| / 2*x*DiracDelta(x)\ | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\||
| | 4*DiracDelta(x)*cos|-----------|*cosh| / ------- *sin|-----------||*sin| / ------- *cos|-----------|| 4*DiracDelta(x)*cos| / ------- *cos|-----------||*sin|-----------|*sinh| / ------- *sin|-----------|| cos |-----------|*|-1 + -----------------|*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------||*sign(x) sin |-----------|*|-1 + -----------------|*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------||*sign(x) |-1 + -----------------|*cos| / ------- *cos|-----------||*sign(x)*sin|-----------|*sinh| / ------- *sin|-----------|| |-1 + -----------------|*cos|-----------|*cosh| / ------- *sin|-----------||*sign(x)*sin| / ------- *cos|-----------|| 2*|-1 + -----------------|*cos|-----------|*sign(x)*sin|-----------|*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------||| / _________ \ / _________ \ |4*DiracDelta(x)*cos|-----------|*cos| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| 4*DiracDelta(x)*cosh| / ------- *sin|-----------||*sin|-----------|*sin| / ------- *cos|-----------|| cos |-----------|*|-1 + -----------------|*sign(x)*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| sin |-----------|*|-1 + -----------------|*sign(x)*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| |-1 + -----------------|*cos|-----------|*cos| / ------- *cos|-----------||*sign(x)*sinh| / ------- *sin|-----------|| |-1 + -----------------|*cosh| / ------- *sin|-----------||*sign(x)*sin|-----------|*sin| / ------- *cos|-----------|| 2*|-1 + -----------------|*cos|-----------|*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------||*sign(x)*sin|-----------|| / _________ \ / _________ \ |-1 + -----------------|*|cos|-----------|*cos| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| + cosh| / ------- *sin|-----------||*sin|-----------|*sin| / ------- *cos|-----------|||*cos|-----------|*cos| / ------- *cos|-----------||*sign(x)*sinh| / ------- *sin|-----------|| |-1 + -----------------|*|cos|-----------|*cos| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| + cosh| / ------- *sin|-----------||*sin|-----------|*sin| / ------- *cos|-----------|||*cosh| / ------- *sin|-----------||*sign(x)*sin|-----------|*sin| / ------- *cos|-----------|| |-1 + -----------------|*|cos|-----------|*cosh| / ------- *sin|-----------||*sin| / ------- *cos|-----------|| - cos| / ------- *cos|-----------||*sin|-----------|*sinh| / ------- *sin|-----------|||*cos|-----------|*cosh| / ------- *sin|-----------||*sign(x)*sin| / ------- *cos|-----------|| |-1 + -----------------|*|cos|-----------|*cosh| / ------- *sin|-----------||*sin| / ------- *cos|-----------|| - cos| / ------- *cos|-----------||*sin|-----------|*sinh| / ------- *sin|-----------|||*cos| / ------- *cos|-----------||*sign(x)*sin|-----------|*sinh| / ------- *sin|-----------|||
| | \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 // \ 2 / \ sign(x) / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \ sign(x) / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ sign(x) / \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 // \ sign(x) / \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ sign(x) / \ 2 / \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 //| | / x /atan2(0, x)\| | / x /atan2(0, x)\| | \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 // \ 2 / \ sign(x) / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \ sign(x) / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ sign(x) / \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ sign(x) / \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 // \ sign(x) / \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 /| | / x /atan2(0, x)\| | / x /atan2(0, x)\| \ sign(x) / \ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ sign(x) / \ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 // \ sign(x) / \ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ sign(x) / \ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 //| / / ___\\
|- |- --------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------|*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------|| - |--------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------|*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\cos\\/ x // 2
| | _________ _________ x x _________ _________ x | \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // | _________ _________ x x _________ _________ x | \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // x x x x | // / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \ / / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \\ // / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \ / / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \\ // / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \ / / _________ \ / _________ \ / _________ \ / _________ \\ / _________ \ / _________ \\
| | / x / x / x / x | | / x / x / x / x | | || /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| | / x /atan2(0, x)\| | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| | / x /atan2(0, x)\|| 3 2/ / ___\\ || /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| | / x /atan2(0, x)\| | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| | / x /atan2(0, x)\|| d / / / ___\\\ || /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| | / x /atan2(0, x)\| | /atan2(0, x)\ | / x /atan2(0, x)\| | / x /atan2(0, x)\| | / x /atan2(0, x)\| /atan2(0, x)\ | / x /atan2(0, x)\|| | / x /atan2(0, x)\| | / x /atan2(0, x)\|| / / ___\\ / ___\
2/ ___\ / ___\ / 2/ ___\\ / ___\ | | / ------- / ------- x* / ------- x* / ------- | | / ------- / ------- x* / ------- x* / ------- | | ||cos|-----------|*cos| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| + cosh| / ------- *sin|-----------||*sin|-----------|*sin| / ------- *cos|-----------|||*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| - |cos|-----------|*cosh| / ------- *sin|-----------||*sin| / ------- *cos|-----------|| - cos| / ------- *cos|-----------||*sin|-----------|*sinh| / ------- *sin|-----------|||*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------||| *sign (x)*sign \cos\\/ x // 2*||cos|-----------|*cos| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| + cosh| / ------- *sin|-----------||*sin|-----------|*sin| / ------- *cos|-----------|||*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| - |cos|-----------|*cosh| / ------- *sin|-----------||*sin| / ------- *cos|-----------|| - cos| / ------- *cos|-----------||*sin|-----------|*sinh| / ------- *sin|-----------|||*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------|||*--\sign\cos\\/ x ///*sign(x) ||cos|-----------|*cos| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| + cosh| / ------- *sin|-----------||*sin|-----------|*sin| / ------- *cos|-----------|||*sin| / ------- *cos|-----------||*sinh| / ------- *sin|-----------|| - |cos|-----------|*cosh| / ------- *sin|-----------||*sin| / ------- *cos|-----------|| - cos| / ------- *cos|-----------||*sin|-----------|*sinh| / ------- *sin|-----------|||*cos| / ------- *cos|-----------||*cosh| / ------- *sin|-----------|||*sign(x)*sign\cos\\/ x //*sin\\/ x /
1 + tan \\/ x / tan\\/ x / 2*\1 + tan \\/ x //*tan\\/ x / \ \ \/ sign(x) \/ sign(x) \/ sign(x) \/ sign(x) / \ \/ sign(x) \/ sign(x) \/ sign(x) \/ sign(x) / / \\ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \\/ sign(x) \ 2 /// \\ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \\/ sign(x) \ 2 /// dx \\ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ \ 2 / \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \\/ sign(x) \ 2 // \ 2 / \\/ sign(x) \ 2 /// \\/ sign(x) \ 2 // \\/ sign(x) \ 2 ///
--------------- - ---------- + ------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x 3/2 ___ | / ___\| / ___\ 2 _________ _________
x \/ x |cos\\/ x /|*cos\\/ x / | / ___\| 2/ ___\ / x | / ___\| / ___\ ___ / x | / ___\| 2/ ___\
x*|cos\\/ x /| *cos \\/ x / / ------- *|cos\\/ x /|*cos\\/ x / \/ x * / ------- *|cos\\/ x /|*cos \\/ x /
\/ sign(x) \/ sign(x)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4
$$\frac{- \frac{\left(- \left(\frac{4 \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \delta\left(x\right)}{\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} + \frac{4 \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \delta\left(x\right)}{\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} - \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} - \frac{2 \left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}}\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \left(- \frac{4 \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \delta\left(x\right)}{\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} + \frac{4 \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \delta\left(x\right)}{\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} + \frac{2 \left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} - \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} - \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}}}\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} + \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} + \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} + \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x} - \frac{\left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \operatorname{sign}{\left(x \right)}}{x}\right) \operatorname{sign}{\left(\cos{\left(\sqrt{x} \right)} \right)}}{\cos{\left(\sqrt{x} \right)} \left|{\cos{\left(\sqrt{x} \right)}}\right|} + \frac{2 \left(\left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} + \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \operatorname{sign}{\left(x \right)} \frac{d}{d x} \operatorname{sign}{\left(\cos{\left(\sqrt{x} \right)} \right)}}{\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\sqrt{x} \right)} \left|{\cos{\left(\sqrt{x} \right)}}\right|} - \frac{\left(\left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} + \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right)^{2} \operatorname{sign}^{3}{\left(x \right)} \operatorname{sign}^{2}{\left(\cos{\left(\sqrt{x} \right)} \right)}}{x \cos^{2}{\left(\sqrt{x} \right)} \left|{\cos{\left(\sqrt{x} \right)}}\right|^{2}} + \frac{\tan^{2}{\left(\sqrt{x} \right)} + 1}{x} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \tan{\left(\sqrt{x} \right)}}{\sqrt{x}} + \frac{\left(\left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} + \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \left(\sin{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} - \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \sinh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \cos{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)} \cosh{\left(\sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \right)}\right) \sin{\left(\sqrt{x} \right)} \operatorname{sign}{\left(x \right)} \operatorname{sign}{\left(\cos{\left(\sqrt{x} \right)} \right)}}{\sqrt{x} \sqrt{\frac{x}{\operatorname{sign}{\left(x \right)}}} \cos^{2}{\left(\sqrt{x} \right)} \left|{\cos{\left(\sqrt{x} \right)}}\right|} - \frac{\tan{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}}{4}$$
Gráfico