Derivada de x^sinx^2

Ha introducido [src]

    2   
 sin (x)
x

$$x^{\sin^{2}{\left(x \right)}}$$

x^(sin(x)^2)

Solución detallada

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Perola derivada

$\left(\log{\left(\sin^{2}{\left(x \right)} \right)} + 1\right) \left|{\sin{\left(x \right)}}\right|^{2 \sin^{2}{\left(x \right)}}$

Respuesta:

$\left(\log{\left(\sin^{2}{\left(x \right)} \right)} + 1\right) \left|{\sin{\left(x \right)}}\right|^{2 \sin^{2}{\left(x \right)}}$

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

    2    /                          2              2                                                           \
 sin (x) |/sin(x)                  \     2      sin (x)        2                  2             4*cos(x)*sin(x)|
x       *||------ + 2*cos(x)*log(x)| *sin (x) - ------- - 2*sin (x)*log(x) + 2*cos (x)*log(x) + ---------------|
         |\  x                     /                2                                                  x       |
         \                                         x                                                           /

$$x^{\sin^{2}{\left(x \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \sin^{2}{\left(x \right)} - 2 \log{\left(x \right)} \sin^{2}{\left(x \right)} + 2 \log{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} - \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right)$$

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Tercera derivada [src]

    2    /                          3                2           2           2                                                                              /   2                                                           \       \
 sin (x) |/sin(x)                  \     3      6*sin (x)   2*sin (x)   6*cos (x)                            6*cos(x)*sin(x)     /sin(x)                  \ |sin (x)        2                  2             4*cos(x)*sin(x)|       |
x       *||------ + 2*cos(x)*log(x)| *sin (x) - --------- + --------- + --------- - 8*cos(x)*log(x)*sin(x) - --------------- - 3*|------ + 2*cos(x)*log(x)|*|------- - 2*cos (x)*log(x) + 2*sin (x)*log(x) - ---------------|*sin(x)|
         |\  x                     /                x            3          x                                        2           \  x                     / |    2                                                  x       |       |
         \                                                      x                                                   x                                       \   x                                                           /       /

$$x^{\sin^{2}{\left(x \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \sin^{3}{\left(x \right)} - 3 \left(2 \log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(2 \log{\left(x \right)} \sin^{2}{\left(x \right)} - 2 \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{\sin^{2}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)} - 8 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \frac{6 \sin^{2}{\left(x \right)}}{x} + \frac{6 \cos^{2}{\left(x \right)}}{x} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin^{2}{\left(x \right)}}{x^{3}}\right)$$

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Gráfico

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Derivada de x^sinx^2

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