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 (60-x)*e^(x+60)
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Derivada de 5*x/(x+1)
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Derivada de 5x^8-8x+1
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Derivada de (5x+7)/(2x-2)
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Expresiones idénticas
- y=x^(cos(x))+(ln(arctg(x^ dos))+(sin(x))^(uno / dos))^(uno / dos)
- y es igual a x en el grado ( coseno de (x)) más (ln(arctg(x al cuadrado )) más ( seno de (x)) en el grado (1 dividir por 2)) en el grado (1 dividir por 2)
- y es igual a x en el grado ( coseno de (x)) más (ln(arctg(x en el grado dos)) más ( seno de (x)) en el grado (uno dividir por dos)) en el grado (uno dividir por dos)
- y=x(cos(x))+(ln(arctg(x2))+(sin(x))(1/2))(1/2)
- y=xcosx+lnarctgx2+sinx1/21/2
- y=x^(cos(x))+(ln(arctg(x²))+(sin(x))^(1/2))^(1/2)
- y=x en el grado (cos(x))+(ln(arctg(x en el grado 2))+(sin(x)) en el grado (1/2)) en el grado (1/2)
- y=x^cosx+lnarctgx^2+sinx^1/2^1/2
- y=x^(cos(x))+(ln(arctg(x^2))+(sin(x))^(1 dividir por 2))^(1 dividir por 2)
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Expresiones semejantes
- y=x^(cos(x))-(ln(arctg(x^2))+(sin(x))^(1/2))^(1/2)
- y=x^(cos(x))+(ln(arctg(x^2))-(sin(x))^(1/2))^(1/2)
- y=x^(cosx)+(ln(arctg(x^2))+(sinx)^(1/2))^(1/2)
Derivada de y=x^(cos(x))+(ln(arctg(x^2))+(sin(x))^(1/2))^(1/2)
Solución
Ha introducido
[src]
____________________________ cos(x) / / / 2\\ ________ x + \/ log\atan\x // + \/ sin(x)
$$x^{\cos{\left(x \right)}} + \sqrt{\log{\left(\operatorname{atan}{\left(x^{2} \right)} \right)} + \sqrt{\sin{\left(x \right)}}}$$
x^cos(x) + sqrt(log(atan(x^2)) + sqrt(sin(x)))
Primera derivada
[src]
cos(x) x
------------ + -----------------
________ / 4\ / 2\
cos(x) /cos(x) \ 4*\/ sin(x) \1 + x /*atan\x /
x *|------ - log(x)*sin(x)| + --------------------------------
\ x / ____________________________
/ / / 2\\ ________
\/ log\atan\x // + \/ sin(x)
$$x^{\cos{\left(x \right)}} \left(- \log{\left(x \right)} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) + \frac{\frac{x}{\left(x^{4} + 1\right) \operatorname{atan}{\left(x^{2} \right)}} + \frac{\cos{\left(x \right)}}{4 \sqrt{\sin{\left(x \right)}}}}{\sqrt{\log{\left(\operatorname{atan}{\left(x^{2} \right)} \right)} + \sqrt{\sin{\left(x \right)}}}}$$
Segunda derivada
[src]
2 2 4
________ cos (x) 8 16*x 32*x 2
2*\/ sin(x) + --------- - ----------------- + ------------------- + ------------------ / cos(x) 4*x \
3/2 / 4\ / 2\ 2 2 |---------- + -----------------|
2 sin (x) \1 + x /*atan\x / / 4\ 2/ 2\ / 4\ / 2\ | ________ / 4\ / 2\|
cos(x) / cos(x)\ cos(x) /cos(x) 2*sin(x)\ \1 + x / *atan \x / \1 + x / *atan\x / \\/ sin(x) \1 + x /*atan\x //
x *|log(x)*sin(x) - ------| - x *|------ + cos(x)*log(x) + --------| - --------------------------------------------------------------------------------------- - ----------------------------------
\ x / | 2 x | ____________________________ 3/2
\ x / / ________ / / 2\\ / ________ / / 2\\\
8*\/ \/ sin(x) + log\atan\x // 16*\\/ sin(x) + log\atan\x ///
$$x^{\cos{\left(x \right)}} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{2} - x^{\cos{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) - \frac{\left(\frac{4 x}{\left(x^{4} + 1\right) \operatorname{atan}{\left(x^{2} \right)}} + \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\right)^{2}}{16 \left(\log{\left(\operatorname{atan}{\left(x^{2} \right)} \right)} + \sqrt{\sin{\left(x \right)}}\right)^{\frac{3}{2}}} - \frac{\frac{32 x^{4}}{\left(x^{4} + 1\right)^{2} \operatorname{atan}{\left(x^{2} \right)}} + \frac{16 x^{2}}{\left(x^{4} + 1\right)^{2} \operatorname{atan}^{2}{\left(x^{2} \right)}} + 2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{8}{\left(x^{4} + 1\right) \operatorname{atan}{\left(x^{2} \right)}}}{8 \sqrt{\log{\left(\operatorname{atan}{\left(x^{2} \right)} \right)} + \sqrt{\sin{\left(x \right)}}}}$$
Tercera derivada
[src]
3 3 3 5 7 / 2 2 4 \
2*cos(x) 3*cos (x) 320*x 96*x 128*x 384*x 512*x 3 / cos(x) 4*x \ | ________ cos (x) 8 16*x 32*x |
---------- + --------- - ------------------ - ------------------- + ------------------- + ------------------- + ------------------ / cos(x) 4*x \ 3*|---------- + -----------------|*|2*\/ sin(x) + --------- - ----------------- + ------------------- + ------------------|
________ 5/2 2 2 3 3 3 3*|---------- + -----------------| | ________ / 4\ / 2\| | 3/2 / 4\ / 2\ 2 2 |
3 \/ sin(x) sin (x) / 4\ / 2\ / 4\ 2/ 2\ / 4\ 3/ 2\ / 4\ 2/ 2\ / 4\ / 2\ | ________ / 4\ / 2\| \\/ sin(x) \1 + x /*atan\x // | sin (x) \1 + x /*atan\x / / 4\ 2/ 2\ / 4\ / 2\|
cos(x) / 3*cos(x) 2*cos(x) 3*sin(x)\ cos(x) / cos(x)\ \1 + x / *atan\x / \1 + x / *atan \x / \1 + x / *atan \x / \1 + x / *atan \x / \1 + x / *atan\x / \\/ sin(x) \1 + x /*atan\x // cos(x) / cos(x)\ /cos(x) 2*sin(x)\ \ \1 + x / *atan \x / \1 + x / *atan\x //
x *|log(x)*sin(x) - -------- + -------- + --------| - x *|log(x)*sin(x) - ------| + ---------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------- + 3*x *|log(x)*sin(x) - ------|*|------ + cos(x)*log(x) + --------| + ----------------------------------------------------------------------------------------------------------------------------
| x 3 2 | \ x / ____________________________ 5/2 \ x / | 2 x | 3/2
\ x x / / ________ / / 2\\ / ________ / / 2\\\ \ x / / ________ / / 2\\\
16*\/ \/ sin(x) + log\atan\x // 64*\\/ sin(x) + log\atan\x /// 32*\\/ sin(x) + log\atan\x ///
$$- x^{\cos{\left(x \right)}} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)^{3} + 3 x^{\cos{\left(x \right)}} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) + x^{\cos{\left(x \right)}} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x} + \frac{3 \sin{\left(x \right)}}{x^{2}} + \frac{2 \cos{\left(x \right)}}{x^{3}}\right) + \frac{3 \left(\frac{4 x}{\left(x^{4} + 1\right) \operatorname{atan}{\left(x^{2} \right)}} + \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\right)^{3}}{64 \left(\log{\left(\operatorname{atan}{\left(x^{2} \right)} \right)} + \sqrt{\sin{\left(x \right)}}\right)^{\frac{5}{2}}} + \frac{3 \left(\frac{4 x}{\left(x^{4} + 1\right) \operatorname{atan}{\left(x^{2} \right)}} + \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\right) \left(\frac{32 x^{4}}{\left(x^{4} + 1\right)^{2} \operatorname{atan}{\left(x^{2} \right)}} + \frac{16 x^{2}}{\left(x^{4} + 1\right)^{2} \operatorname{atan}^{2}{\left(x^{2} \right)}} + 2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{8}{\left(x^{4} + 1\right) \operatorname{atan}{\left(x^{2} \right)}}\right)}{32 \left(\log{\left(\operatorname{atan}{\left(x^{2} \right)} \right)} + \sqrt{\sin{\left(x \right)}}\right)^{\frac{3}{2}}} + \frac{\frac{512 x^{7}}{\left(x^{4} + 1\right)^{3} \operatorname{atan}{\left(x^{2} \right)}} + \frac{384 x^{5}}{\left(x^{4} + 1\right)^{3} \operatorname{atan}^{2}{\left(x^{2} \right)}} - \frac{320 x^{3}}{\left(x^{4} + 1\right)^{2} \operatorname{atan}{\left(x^{2} \right)}} + \frac{128 x^{3}}{\left(x^{4} + 1\right)^{3} \operatorname{atan}^{3}{\left(x^{2} \right)}} - \frac{96 x}{\left(x^{4} + 1\right)^{2} \operatorname{atan}^{2}{\left(x^{2} \right)}} + \frac{2 \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{3 \cos^{3}{\left(x \right)}}{\sin^{\frac{5}{2}}{\left(x \right)}}}{16 \sqrt{\log{\left(\operatorname{atan}{\left(x^{2} \right)} \right)} + \sqrt{\sin{\left(x \right)}}}}$$
Gráfico