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y=(sin^-1x)^cosx
Derivada de la función/ sin^-1x/ y=(sin^-1x)^cosx

Derivada de y=(sin^-1x)^cosx

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src] 
        cos(x)
/  1   \      
|------|      
\sin(x)/
(1sin⁡(x))cos⁡(x)\left(\frac{1}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}} 
(1/sin(x))^cos(x)
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-200200
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Trazar el gráfico f'(x)
Primera derivada [src] 
        cos(x) /     2                        \
/  1   \       |  cos (x)      /  1   \       |
|------|      *|- ------- - log|------|*sin(x)|
\sin(x)/       \   sin(x)      \sin(x)/       /
(−log⁡(1sin⁡(x))sin⁡(x)−cos⁡2(x)sin⁡(x))(1sin⁡(x))cos⁡(x)\left(- \log{\left(\frac{1}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\frac{1}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}}
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Segunda derivada [src] 
               /                              2                                     \
        cos(x) |/   2                        \    /                     2   \       |
/  1   \       ||cos (x)      /  1   \       |    |       /  1   \   cos (x)|       |
|------|      *||------- + log|------|*sin(x)|  + |3 - log|------| + -------|*cos(x)|
\sin(x)/       |\ sin(x)      \sin(x)/       /    |       \sin(x)/      2   |       |
               \                                  \                  sin (x)/       /
((log⁡(1sin⁡(x))sin⁡(x)+cos⁡2(x)sin⁡(x))2+(−log⁡(1sin⁡(x))+3+cos⁡2(x)sin⁡2(x))cos⁡(x))(1sin⁡(x))cos⁡(x)\left(\left(\log{\left(\frac{1}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + \left(- \log{\left(\frac{1}{\sin{\left(x \right)}} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}\right) \left(\frac{1}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}}
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Tercera derivada [src] 
                /                              3                                                                                                                              \
         cos(x) |/   2                        \                                         2           4        /   2                        \ /                     2   \       |
 /  1   \       ||cos (x)      /  1   \       |                  /  1   \          2*cos (x)   2*cos (x)     |cos (x)      /  1   \       | |       /  1   \   cos (x)|       |
-|------|      *||------- + log|------|*sin(x)|  + 3*sin(x) - log|------|*sin(x) + --------- + --------- + 3*|------- + log|------|*sin(x)|*|3 - log|------| + -------|*cos(x)|
 \sin(x)/       |\ sin(x)      \sin(x)/       /                  \sin(x)/            sin(x)        3         \ sin(x)      \sin(x)/       / |       \sin(x)/      2   |       |
                \                                                                               sin (x)                                     \                  sin (x)/       /
−((log⁡(1sin⁡(x))sin⁡(x)+cos⁡2(x)sin⁡(x))3+3(log⁡(1sin⁡(x))sin⁡(x)+cos⁡2(x)sin⁡(x))(−log⁡(1sin⁡(x))+3+cos⁡2(x)sin⁡2(x))cos⁡(x)−log⁡(1sin⁡(x))sin⁡(x)+3sin⁡(x)+2cos⁡2(x)sin⁡(x)+2cos⁡4(x)sin⁡3(x))(1sin⁡(x))cos⁡(x)- \left(\left(\log{\left(\frac{1}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} + 3 \left(\log{\left(\frac{1}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(- \log{\left(\frac{1}{\sin{\left(x \right)}} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} - \log{\left(\frac{1}{\sin{\left(x \right)}} \right)} \sin{\left(x \right)} + 3 \sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \left(\frac{1}{\sin{\left(x \right)}}\right)^{\cos{\left(x \right)}}
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Gráfico
Derivada de y=(sin^-1x)^cosx
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