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:
-
Derivada de x^-(4/5)
-
Derivada de x^-8
-
Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=arctg(cosx)^(uno /x)
- y es igual a arctg( coseno de x) en el grado (1 dividir por x)
- y es igual a arctg( coseno de x) en el grado (uno dividir por x)
- y=arctg(cosx)(1/x)
- y=arctgcosx1/x
- y=arctgcosx^1/x
- y=arctg(cosx)^(1 dividir por x)
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Expresiones con funciones
- arctg
- arctg^2(1/x)
Derivada de y=arctg(cosx)^(1/x)
Solución
Ha introducido
[src]
x ______________ \/ atan(cos(x))
$$\operatorname{atan}^{\frac{1}{x}}{\left(\cos{\left(x \right)} \right)}$$
atan(cos(x))^(1/x)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
x ______________ / log(atan(cos(x))) sin(x) \
\/ atan(cos(x)) *|- ----------------- - ----------------------------|
| 2 / 2 \ |
\ x x*\1 + cos (x)/*atan(cos(x))/
$$\left(- \frac{\sin{\left(x \right)}}{x \left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{\log{\left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\frac{1}{x}}{\left(\cos{\left(x \right)} \right)}$$
Segunda derivada
[src]
/ 2 \
|/log(atan(cos(x))) sin(x) \ |
||----------------- + --------------------------| |
|| x / 2 \ | 2 2 |
x ______________ |\ \1 + cos (x)/*atan(cos(x))/ 2*log(atan(cos(x))) cos(x) sin (x) 2*sin (x)*cos(x) 2*sin(x) |
\/ atan(cos(x)) *|------------------------------------------------- + ------------------- - -------------------------- - ---------------------------- - --------------------------- + ----------------------------|
| x 2 / 2 \ 2 2 / 2 \ |
| x \1 + cos (x)/*atan(cos(x)) / 2 \ 2 / 2 \ x*\1 + cos (x)/*atan(cos(x))|
\ \1 + cos (x)/ *atan (cos(x)) \1 + cos (x)/ *atan(cos(x)) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{\left(- \frac{\cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{2 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{\sin^{2}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}^{2}{\left(\cos{\left(x \right)} \right)}} + \frac{\left(\frac{\sin{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{\log{\left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} \right)}}{x}\right)^{2}}{x} + \frac{2 \sin{\left(x \right)}}{x \left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\frac{1}{x}}{\left(\cos{\left(x \right)} \right)}}{x}$$
Tercera derivada
[src]
/ / 2 2 \ \
| 3 /log(atan(cos(x))) sin(x) \ | 2*log(atan(cos(x))) cos(x) sin (x) 2*sin(x) 2*sin (x)*cos(x) | |
| /log(atan(cos(x))) sin(x) \ 3*|----------------- + --------------------------|*|- ------------------- + -------------------------- + ---------------------------- - ---------------------------- + ---------------------------| |
| |----------------- + --------------------------| | x / 2 \ | | 2 / 2 \ 2 / 2 \ 2 | |
| | x / 2 \ | 3 3 \ \1 + cos (x)/*atan(cos(x))/ | x \1 + cos (x)/*atan(cos(x)) / 2 \ 2 x*\1 + cos (x)/*atan(cos(x)) / 2 \ | 2 3 3 2 2 2 |
x ______________ | \ \1 + cos (x)/*atan(cos(x))/ 6*log(atan(cos(x))) sin(x) 2*sin (x) 2*sin (x) \ \1 + cos (x)/ *atan (cos(x)) \1 + cos (x)/ *atan(cos(x))/ 8*cos (x)*sin (x) 6*sin(x) 6*sin (x)*cos(x) 6*cos (x)*sin(x) 3*cos(x)*sin(x) 3*cos(x) 3*sin (x) 6*sin (x)*cos(x) |
\/ atan(cos(x)) *|- ------------------------------------------------- - ------------------- + -------------------------- - ---------------------------- + --------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------- - ----------------------------- - ---------------------------- - --------------------------- - ---------------------------- + ---------------------------- + ------------------------------ + -----------------------------|
| 2 3 / 2 \ 3 2 x 3 2 / 2 \ 3 2 2 / 2 \ 2 2 |
| x x \1 + cos (x)/*atan(cos(x)) / 2 \ 3 / 2 \ / 2 \ x *\1 + cos (x)/*atan(cos(x)) / 2 \ 2 / 2 \ / 2 \ 2 x*\1 + cos (x)/*atan(cos(x)) / 2 \ 2 / 2 \ |
\ \1 + cos (x)/ *atan (cos(x)) \1 + cos (x)/ *atan(cos(x)) \1 + cos (x)/ *atan(cos(x)) \1 + cos (x)/ *atan (cos(x)) \1 + cos (x)/ *atan(cos(x)) \1 + cos (x)/ *atan (cos(x)) x*\1 + cos (x)/ *atan (cos(x)) x*\1 + cos (x)/ *atan(cos(x))/
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{\left(\frac{\sin{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{2 \sin^{3}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{6 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{3 \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}^{2}{\left(\cos{\left(x \right)} \right)}} - \frac{8 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{3} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{6 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{3} \operatorname{atan}^{2}{\left(\cos{\left(x \right)} \right)}} - \frac{2 \sin^{3}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{3} \operatorname{atan}^{3}{\left(\cos{\left(x \right)} \right)}} + \frac{3 \left(\frac{\sin{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{\log{\left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} \right)}}{x}\right) \left(\frac{\cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{2 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{\sin^{2}{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}^{2}{\left(\cos{\left(x \right)} \right)}} - \frac{2 \sin{\left(x \right)}}{x \left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{2 \log{\left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} \right)}}{x^{2}}\right)}{x} + \frac{3 \cos{\left(x \right)}}{x \left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{6 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{x \left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{3 \sin^{2}{\left(x \right)}}{x \left(\cos^{2}{\left(x \right)} + 1\right)^{2} \operatorname{atan}^{2}{\left(\cos{\left(x \right)} \right)}} - \frac{\left(\frac{\sin{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} + \frac{\log{\left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} \right)}}{x}\right)^{3}}{x^{2}} - \frac{6 \sin{\left(x \right)}}{x^{2} \left(\cos^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(\cos{\left(x \right)} \right)}} - \frac{6 \log{\left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} \right)}}{x^{3}}\right) \operatorname{atan}^{\frac{1}{x}}{\left(\cos{\left(x \right)} \right)}}{x}$$
Gráfico