Derivada de √x^sin^2x

Ha introducido [src]

        2   
     sin (x)
  ___       
\/ x

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

(sqrt(x))^(sin(x)^2)

Solución detallada

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

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

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

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Gráfico

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Derivada de √x^sin^2x

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