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 2*cos(3*x)
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Derivada de x^(7/6)
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Derivada de (x^2)/4
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Derivada de t
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Expresiones idénticas
- y=(tgx)^(uno / dos)(ln)arctg(x)
- y es igual a (tgx) en el grado (1 dividir por 2)(ln)arctg(x)
- y es igual a (tgx) en el grado (uno dividir por dos)(ln)arctg(x)
- y=(tgx)(1/2)(ln)arctg(x)
- y=tgx1/2lnarctgx
- y=tgx^1/2lnarctgx
- y=(tgx)^(1 dividir por 2)(ln)arctg(x)
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Expresiones con funciones
- ln
- ln(x+k)
- ln4x
- ln(3/x)
- ln√(x-1)
- ln(16+9x^2)
Derivada de y=(tgx)^(1/2)(ln)arctg(x)
Solución
Ha introducido
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________ \/ tan(x) *log(x)*atan(x)
$$\log{\left(x \right)} \sqrt{\tan{\left(x \right)}} \operatorname{atan}{\left(x \right)}$$
(sqrt(tan(x))*log(x))*atan(x)
Primera derivada
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/ / 2 \ \ | |1 tan (x)| | | ________ |- + -------|*log(x)| ________ |\/ tan(x) \2 2 / | \/ tan(x) *log(x) |---------- + --------------------|*atan(x) + ----------------- | x ________ | 2 \ \/ tan(x) / 1 + x
$$\left(\frac{\left(\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}\right) \log{\left(x \right)}}{\sqrt{\tan{\left(x \right)}}} + \frac{\sqrt{\tan{\left(x \right)}}}{x}\right) \operatorname{atan}{\left(x \right)} + \frac{\log{\left(x \right)} \sqrt{\tan{\left(x \right)}}}{x^{2} + 1}$$
Segunda derivada
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________ / 2 \ / ________ / 2 \ / 2 \\
2*\/ tan(x) \1 + tan (x)/*log(x) |4*\/ tan(x) / 2 \ | ________ 1 + tan (x)| 4*\1 + tan (x)/|
------------ + -------------------- |------------ + \1 + tan (x)/*|- 4*\/ tan(x) + -----------|*log(x) - ---------------|*atan(x)
x ________ | 2 | 3/2 | ________ | ________
\/ tan(x) \ x \ tan (x) / x*\/ tan(x) / 2*x*\/ tan(x) *log(x)
----------------------------------- - ---------------------------------------------------------------------------------------------- - ---------------------
2 4 2
1 + x / 2\
\1 + x /
$$- \frac{2 x \log{\left(x \right)} \sqrt{\tan{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}} - \frac{\left(\left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \sqrt{\tan{\left(x \right)}}} + \frac{4 \sqrt{\tan{\left(x \right)}}}{x^{2}}\right) \operatorname{atan}{\left(x \right)}}{4} + \frac{\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\tan{\left(x \right)}}} + \frac{2 \sqrt{\tan{\left(x \right)}}}{x}}{x^{2} + 1}$$
Tercera derivada
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/ / 2 \\
| / 2 \ | ________ 1 + tan (x)||
| / 2\ 6*\1 + tan (x)/*|- 4*\/ tan(x) + -----------||
/ ________ / 2 \ / 2 \\ | ________ | / 2 \ / 2 \ | / 2 \ | 3/2 || / ________ / 2 \ \ / 2 \
|4*\/ tan(x) / 2 \ | ________ 1 + tan (x)| 4*\1 + tan (x)/| |16*\/ tan(x) / 2 \ | 3/2 4*\1 + tan (x)/ 3*\1 + tan (x)/ | 12*\1 + tan (x)/ \ tan (x) /| |2*\/ tan(x) \1 + tan (x)/*log(x)| ________ | 4*x |
3*|------------ + \1 + tan (x)/*|- 4*\/ tan(x) + -----------|*log(x) - ---------------| |------------- + \1 + tan (x)/*|16*tan (x) - --------------- + ----------------|*log(x) - ---------------- - ----------------------------------------------|*atan(x) 3*x*|------------ + --------------------| 2*\/ tan(x) *|-1 + ------|*log(x)
| 2 | 3/2 | ________ | | 3 | ________ 5/2 | 2 ________ x | | x ________ | | 2|
\ x \ tan (x) / x*\/ tan(x) / \ x \ \/ tan(x) tan (x) / x *\/ tan(x) / \ \/ tan(x) / \ 1 + x /
- ---------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------- + ---------------------------------
/ 2\ 8 2 2
4*\1 + x / / 2\ / 2\
\1 + x / \1 + x /
$$- \frac{3 x \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\tan{\left(x \right)}}} + \frac{2 \sqrt{\tan{\left(x \right)}}}{x}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 16 \tan^{\frac{3}{2}}{\left(x \right)}\right) \log{\left(x \right)} - \frac{6 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} \sqrt{\tan{\left(x \right)}}} + \frac{16 \sqrt{\tan{\left(x \right)}}}{x^{3}}\right) \operatorname{atan}{\left(x \right)}}{8} - \frac{3 \left(\left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \sqrt{\tan{\left(x \right)}}} + \frac{4 \sqrt{\tan{\left(x \right)}}}{x^{2}}\right)}{4 \left(x^{2} + 1\right)} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(x \right)} \sqrt{\tan{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}}$$
Gráfico