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

Derivada de y=x^sin^-1x

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

Gráfico:

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Solución

Ha introducido [src] 
   1   
 ------
 sin(x)
x
x1sin⁡(x)x^{\frac{1}{\sin{\left(x \right)}}} 
x^(1/sin(x))
Solución detallada

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-2e522e52
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   1                              
 ------                           
 sin(x) /   1       cos(x)*log(x)\
x      *|-------- - -------------|
        |x*sin(x)         2      |
        \              sin (x)   /
x1sin⁡(x)(−log⁡(x)cos⁡(x)sin⁡2(x)+1xsin⁡(x))x^{\frac{1}{\sin{\left(x \right)}}} \left(- \frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{x \sin{\left(x \right)}}\right)
Simplificar
Segunda derivada [src] 
        /                            2                                       \
   1    |       /  1   cos(x)*log(x)\                                        |
 ------ |       |- - + -------------|                    2                   |
 sin(x) |  1    \  x       sin(x)   /    2*cos(x)   2*cos (x)*log(x)         |
x      *|- -- + ---------------------- - -------- + ---------------- + log(x)|
        |   2           sin(x)           x*sin(x)          2                 |
        \  x                                            sin (x)              /
------------------------------------------------------------------------------
                                    sin(x)
x1sin⁡(x)((log⁡(x)cos⁡(x)sin⁡(x)−1x)2sin⁡(x)+log⁡(x)+2log⁡(x)cos⁡2(x)sin⁡2(x)−2cos⁡(x)xsin⁡(x)−1x2)sin⁡(x)\frac{x^{\frac{1}{\sin{\left(x \right)}}} \left(\frac{\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{1}{x}\right)^{2}}{\sin{\left(x \right)}} + \log{\left(x \right)} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{1}{x^{2}}\right)}{\sin{\left(x \right)}}
Simplificar
Tercera derivada [src] 
        /                                                                                               /                       2                   \                        \
        |                              3                                          /  1   cos(x)*log(x)\ |  1    2*cos(x)   2*cos (x)*log(x)         |                        |
   1    |         /  1   cos(x)*log(x)\                                         3*|- - + -------------|*|- -- - -------- + ---------------- + log(x)|                        |
 ------ |         |- - + -------------|         3                                 \  x       sin(x)   / |   2   x*sin(x)          2                 |                    2   |
 sin(x) |2    3   \  x       sin(x)   /    6*cos (x)*log(x)   5*cos(x)*log(x)                           \  x                   sin (x)              /    3*cos(x)   6*cos (x)|
x      *|-- + - - ---------------------- - ---------------- - --------------- - --------------------------------------------------------------------- + --------- + ---------|
        | 3   x             2                     3                sin(x)                                       sin(x)                                   2               2   |
        \x               sin (x)               sin (x)                                                                                                  x *sin(x)   x*sin (x)/
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                    sin(x)
x1sin⁡(x)(−(log⁡(x)cos⁡(x)sin⁡(x)−1x)3sin⁡2(x)−3(log⁡(x)cos⁡(x)sin⁡(x)−1x)(log⁡(x)+2log⁡(x)cos⁡2(x)sin⁡2(x)−2cos⁡(x)xsin⁡(x)−1x2)sin⁡(x)−5log⁡(x)cos⁡(x)sin⁡(x)−6log⁡(x)cos⁡3(x)sin⁡3(x)+3x+6cos⁡2(x)xsin⁡2(x)+3cos⁡(x)x2sin⁡(x)+2x3)sin⁡(x)\frac{x^{\frac{1}{\sin{\left(x \right)}}} \left(- \frac{\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{1}{x}\right)^{3}}{\sin^{2}{\left(x \right)}} - \frac{3 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{1}{x}\right) \left(\log{\left(x \right)} + \frac{2 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{1}{x^{2}}\right)}{\sin{\left(x \right)}} - \frac{5 \log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{6 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{3}{x} + \frac{6 \cos^{2}{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{3 \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2}{x^{3}}\right)}{\sin{\left(x \right)}}
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Gráfico
Derivada de y=x^sin^-1x
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