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
-
¿Cómo usar?
- Derivada de:
-
Derivada de e^x*sin(x)
-
Derivada de x*e^(1/x)
- Derivada de x!
-
Derivada de e^y
-
Expresiones idénticas
- y=((cos^ tres)x)^(lnx)
- y es igual a (( coseno de al cubo )x) en el grado (lnx)
- y es igual a (( coseno de en el grado tres)x) en el grado (lnx)
- y=((cos3)x)(lnx)
- y=cos3xlnx
- y=((cos³)x)^(lnx)
- y=((cos en el grado 3)x) en el grado (lnx)
- y=cos^3x^lnx
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Expresiones con funciones
- Coseno cos
- cos(3)^(2)*x
- cos2
- cos(5-3*x)
- cos(x)^(100)
- cos/sin
Derivada de y=((cos^3)x)^(lnx)
Solución
Ha introducido
[src]
log(x) / 3 \ \cos (x)*x/
$$\left(x \cos^{3}{\left(x \right)}\right)^{\log{\left(x \right)}}$$
(cos(x)^3*x)^log(x)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
log(x) / / 3 \ / 3 2 \ \
/ 3 \ |log\cos (x)*x/ \cos (x) - 3*x*cos (x)*sin(x)/*log(x)|
\cos (x)*x/ *|-------------- + -------------------------------------|
| x 3 |
\ x*cos (x) /
$$\left(x \cos^{3}{\left(x \right)}\right)^{\log{\left(x \right)}} \left(\frac{\left(- 3 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{3}{\left(x \right)}\right) \log{\left(x \right)}}{x \cos^{3}{\left(x \right)}} + \frac{\log{\left(x \cos^{3}{\left(x \right)} \right)}}{x}\right)$$
Segunda derivada
[src]
/ 2 \
|/ / 3 \ (-cos(x) + 3*x*sin(x))*log(x)\ |
log(x) ||- log\x*cos (x)/ + -----------------------------| / 3 \ / 2 2 \ |
/ 3 \ |\ cos(x) / log\x*cos (x)/ 3*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x) 2*(-cos(x) + 3*x*sin(x)) (-cos(x) + 3*x*sin(x))*log(x) 3*(-cos(x) + 3*x*sin(x))*log(x)*sin(x)|
\x*cos (x)/ *|--------------------------------------------------- - -------------- - ---------------------------------------------------- - ------------------------ + ----------------------------- - --------------------------------------|
| x x 2 x*cos(x) x*cos(x) 2 |
\ cos (x) cos (x) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{\left(x \cos^{3}{\left(x \right)}\right)^{\log{\left(x \right)}} \left(- \frac{3 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \frac{3 \left(- 2 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \log{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x \cos{\left(x \right)}} + \frac{\left(\frac{\left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(x \cos^{3}{\left(x \right)} \right)}\right)^{2}}{x} - \frac{\log{\left(x \cos^{3}{\left(x \right)} \right)}}{x}\right)}{x}$$
Tercera derivada
[src]
/ / / 3 \ / 2 2 \ \ \
| 3 / / 3 \ (-cos(x) + 3*x*sin(x))*log(x)\ |log\x*cos (x)/ 2*(-cos(x) + 3*x*sin(x)) 3*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x) (-cos(x) + 3*x*sin(x))*log(x) 3*(-cos(x) + 3*x*sin(x))*log(x)*sin(x)| |
| / / 3 \ (-cos(x) + 3*x*sin(x))*log(x)\ 3*|- log\x*cos (x)/ + -----------------------------|*|-------------- + ------------------------ + ---------------------------------------------------- - ----------------------------- + --------------------------------------| |
log(x) | |- log\x*cos (x)/ + -----------------------------| / 3 \ / 2 2 \ / 3 2 3 2 \ \ cos(x) / | x x*cos(x) 2 x*cos(x) 2 | / 2 2 \ 2 / 2 2 \ |
/ 3 \ | \ cos(x) / 2*log\x*cos (x)/ 9*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/ 3*(-cos(x) + 3*x*sin(x))*log(x) 3*\3*cos (x) - 6*sin (x)*cos(x) + 2*x*sin (x) - 7*x*cos (x)*sin(x)/*log(x) \ cos (x) cos (x) / 6*(-cos(x) + 3*x*sin(x)) 18*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x)*sin(x) 12*sin (x)*(-cos(x) + 3*x*sin(x))*log(x) 9*(-cos(x) + 3*x*sin(x))*sin(x) 2*(-cos(x) + 3*x*sin(x))*log(x) 6*\x*cos (x) - 2*x*sin (x) + 2*cos(x)*sin(x)/*log(x) 6*(-cos(x) + 3*x*sin(x))*log(x)*sin(x)|
\x*cos (x)/ *|- --------------------------------------------------- + ---------------- - --------------------------------------------- - ------------------------------- - -------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------ - ------------------------------------------------------------ - ---------------------------------------- - ------------------------------- - ------------------------------- + ---------------------------------------------------- + --------------------------------------|
| 2 2 2 cos(x) 3 x 2 3 3 2 2 2 2 |
\ x x x*cos (x) cos (x) x *cos(x) cos (x) cos (x) x*cos (x) x *cos(x) x*cos (x) x*cos (x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{\left(x \cos^{3}{\left(x \right)}\right)^{\log{\left(x \right)}} \left(- \frac{12 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)} \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{3 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)}}{\cos{\left(x \right)}} - \frac{18 \left(- 2 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \log{\left(x \right)} \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{3 \left(2 x \sin^{3}{\left(x \right)} - 7 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} - 6 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 \cos^{3}{\left(x \right)}\right) \log{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{6 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)} \sin{\left(x \right)}}{x \cos^{2}{\left(x \right)}} - \frac{9 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{x \cos^{2}{\left(x \right)}} + \frac{3 \left(\frac{\left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(x \cos^{3}{\left(x \right)} \right)}\right) \left(\frac{3 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{3 \left(- 2 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \log{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \frac{\left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)}}{x \cos{\left(x \right)}} + \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x \cos{\left(x \right)}} + \frac{\log{\left(x \cos^{3}{\left(x \right)} \right)}}{x}\right)}{x} + \frac{6 \left(- 2 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \log{\left(x \right)}}{x \cos^{2}{\left(x \right)}} - \frac{9 \left(- 2 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{x \cos^{2}{\left(x \right)}} - \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)}}{x^{2} \cos{\left(x \right)}} + \frac{6 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2} \cos{\left(x \right)}} - \frac{\left(\frac{\left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(x \cos^{3}{\left(x \right)} \right)}\right)^{3}}{x^{2}} + \frac{2 \log{\left(x \cos^{3}{\left(x \right)} \right)}}{x^{2}}\right)}{x}$$
Gráfico