Derivada de y=cosx^x

Ha introducido [src]

   x   
cos (x)

$$\cos^{x}{\left(x \right)}$$

cos(x)^x

Solución detallada

No logro encontrar los pasos en la búsqueda de esta derivada.

Perola derivada

$x^{x} \left(\log{\left(x \right)} + 1\right)$

Respuesta:

$x^{x} \left(\log{\left(x \right)} + 1\right)$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   x    /  x*sin(x)              \
cos (x)*|- -------- + log(cos(x))|
        \   cos(x)               /

$$\left(- \frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} + \log{\left(\cos{\left(x \right)} \right)}\right) \cos^{x}{\left(x \right)}$$

Simplificar

Segunda derivada [src]

        /                         2                       2   \
   x    |/               x*sin(x)\        2*sin(x)   x*sin (x)|
cos (x)*||-log(cos(x)) + --------|  - x - -------- - ---------|
        |\                cos(x) /         cos(x)        2    |
        \                                             cos (x) /

$$\left(- \frac{x \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - x + \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right)^{2} - \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{x}{\left(x \right)}$$

Simplificar

3-я производная [src]

        /                              3        2                                  /                    2   \                       3   \
   x    |     /               x*sin(x)\    3*sin (x)     /               x*sin(x)\ |    2*sin(x)   x*sin (x)|   2*x*sin(x)   2*x*sin (x)|
cos (x)*|-3 - |-log(cos(x)) + --------|  - --------- + 3*|-log(cos(x)) + --------|*|x + -------- + ---------| - ---------- - -----------|
        |     \                cos(x) /        2         \                cos(x) / |     cos(x)        2    |     cos(x)          3     |
        \                                   cos (x)                                \                cos (x) /                  cos (x)  /

$$\left(- \frac{2 x \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right) \left(\frac{x \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + x + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) - \frac{3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 3\right) \cos^{x}{\left(x \right)}$$

Simplificar

Tercera derivada [src]

        /                              3        2                                  /                    2   \                       3   \
   x    |     /               x*sin(x)\    3*sin (x)     /               x*sin(x)\ |    2*sin(x)   x*sin (x)|   2*x*sin(x)   2*x*sin (x)|
cos (x)*|-3 - |-log(cos(x)) + --------|  - --------- + 3*|-log(cos(x)) + --------|*|x + -------- + ---------| - ---------- - -----------|
        |     \                cos(x) /        2         \                cos(x) / |     cos(x)        2    |     cos(x)          3     |
        \                                   cos (x)                                \                cos (x) /                  cos (x)  /

$$\left(- \frac{2 x \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \log{\left(\cos{\left(x \right)} \right)}\right) \left(\frac{x \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + x + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) - \frac{3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 3\right) \cos^{x}{\left(x \right)}$$

Simplificar

Gráfico

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Derivada de y=cosx^x

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Solución