Derivada de y=cos5x^sin3√x

Ha introducido [src]

             /    ___\
          sin\3*\/ x /
(cos(5*x))

\cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}

cos(5*x)^sin(3*sqrt(x))

Solución detallada

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

Perola derivada

$\left(\log{\left(\sin{\left(3 \sqrt{x} \right)} \right)} + 1\right) \sin^{\sin{\left(3 \sqrt{x} \right)}}{\left(3 \sqrt{x} \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(3 \sqrt{x} \right)} \right)} + 1\right) \sin^{\sin{\left(3 \sqrt{x} \right)}}{\left(3 \sqrt{x} \right)}$

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

             /    ___\ /       /    ___\                 /    ___\              \
          sin\3*\/ x / |  5*sin\3*\/ x /*sin(5*x)   3*cos\3*\/ x /*log(cos(5*x))|
(cos(5*x))            *|- ----------------------- + ----------------------------|
                       |          cos(5*x)                        ___           |
                       \                                      2*\/ x            /

\left(- \frac{5 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} + \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{2 \sqrt{x}}\right) \cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}

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Segunda derivada [src]

                       /                                                                               2                                                                                                                     \
                       |                    /       /    ___\                       /    ___\         \                                                                                                                      |
                       |                    |  3*cos\3*\/ x /*log(cos(5*x))   10*sin\3*\/ x /*sin(5*x)|                                                                                                                      |
                       |                    |- ---------------------------- + ------------------------|                                                                                                                      |
             /    ___\ |                    |               ___                       cos(5*x)        |          2         /    ___\                      /    ___\        /    ___\                       /    ___\         |
          sin\3*\/ x / |        /    ___\   \             \/ x                                        /    25*sin (5*x)*sin\3*\/ x /   9*log(cos(5*x))*sin\3*\/ x /   3*cos\3*\/ x /*log(cos(5*x))   15*cos\3*\/ x /*sin(5*x)|
(cos(5*x))            *|- 25*sin\3*\/ x / + ------------------------------------------------------------ - ------------------------- - ---------------------------- - ---------------------------- - ------------------------|
                       |                                                 4                                            2                            4*x                              3/2                     ___              |
                       \                                                                                           cos (5*x)                                                     4*x                      \/ x *cos(5*x)     /

\left(\frac{\left(\frac{10 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x}}\right)^{2}}{4} - \frac{25 \sin{\left(3 \sqrt{x} \right)} \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} - 25 \sin{\left(3 \sqrt{x} \right)} - \frac{9 \log{\left(\cos{\left(5 x \right)} \right)} \sin{\left(3 \sqrt{x} \right)}}{4 x} - \frac{15 \sin{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x} \cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{4 x^{\frac{3}{2}}}\right) \cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}

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Tercera derivada [src]

                       /                                                             3                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \
                       |  /       /    ___\                       /    ___\         \                         /       /    ___\                       /    ___\         \ /                        /    ___\                                    /    ___\          2         /    ___\         /    ___\         \                                                                                                                                                                                                                                            |
                       |  |  3*cos\3*\/ x /*log(cos(5*x))   10*sin\3*\/ x /*sin(5*x)|                         |  3*cos\3*\/ x /*log(cos(5*x))   10*sin\3*\/ x /*sin(5*x)| |       /    ___\   3*cos\3*\/ x /*log(cos(5*x))   9*log(cos(5*x))*sin\3*\/ x /   100*sin (5*x)*sin\3*\/ x /   60*cos\3*\/ x /*sin(5*x)|                                                                                                                                                                                                                                            |
                       |  |- ---------------------------- + ------------------------|                       3*|- ---------------------------- + ------------------------|*|100*sin\3*\/ x / + ---------------------------- + ---------------------------- + -------------------------- + ------------------------|                                                                                                                                                                                                                                            |
             /    ___\ |  |               ___                       cos(5*x)        |           /    ___\     |               ___                       cos(5*x)        | |                                3/2                            x                            2                        ___              |          /    ___\                   3         /    ___\         /    ___\                      /    ___\                                     /    ___\          2         /    ___\         /    ___\                   /    ___\         |
          sin\3*\/ x / |  \             \/ x                                        /    225*cos\3*\/ x /     \             \/ x                                        / \                               x                                                         cos (5*x)                 \/ x *cos(5*x)     /   250*sin\3*\/ x /*sin(5*x)   250*sin (5*x)*sin\3*\/ x /   27*cos\3*\/ x /*log(cos(5*x))   9*cos\3*\/ x /*log(cos(5*x))   27*log(cos(5*x))*sin\3*\/ x /   225*sin (5*x)*cos\3*\/ x /   45*cos\3*\/ x /*sin(5*x)   135*sin\3*\/ x /*sin(5*x)|
(cos(5*x))            *|- ------------------------------------------------------------ - ---------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------- - -------------------------- - ----------------------------- + ---------------------------- + ----------------------------- - -------------------------- + ------------------------ + -------------------------|
                       |                               8                                         ___                                                                                                          8                                                                                                               cos(5*x)                      3                                3/2                            5/2                              2                       ___    2                    3/2                        4*x*cos(5*x)      |
                       \                                                                     2*\/ x                                                                                                                                                                                                                                                      cos (5*x)                        8*x                            8*x                              8*x                    2*\/ x *cos (5*x)            4*x   *cos(5*x)                                 /

\left(- \frac{\left(\frac{10 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x}}\right)^{3}}{8} + \frac{3 \left(\frac{10 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x}}\right) \left(\frac{100 \sin{\left(3 \sqrt{x} \right)} \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 100 \sin{\left(3 \sqrt{x} \right)} + \frac{9 \log{\left(\cos{\left(5 x \right)} \right)} \sin{\left(3 \sqrt{x} \right)}}{x} + \frac{60 \sin{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x} \cos{\left(5 x \right)}} + \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{x^{\frac{3}{2}}}\right)}{8} - \frac{250 \sin{\left(3 \sqrt{x} \right)} \sin^{3}{\left(5 x \right)}}{\cos^{3}{\left(5 x \right)}} - \frac{250 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} + \frac{135 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{4 x \cos{\left(5 x \right)}} + \frac{27 \log{\left(\cos{\left(5 x \right)} \right)} \sin{\left(3 \sqrt{x} \right)}}{8 x^{2}} - \frac{225 \sin^{2}{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{2 \sqrt{x} \cos^{2}{\left(5 x \right)}} - \frac{225 \cos{\left(3 \sqrt{x} \right)}}{2 \sqrt{x}} - \frac{27 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{8 x^{\frac{3}{2}}} + \frac{45 \sin{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{4 x^{\frac{3}{2}} \cos{\left(5 x \right)}} + \frac{9 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{8 x^{\frac{5}{2}}}\right) \cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}

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Derivada de y=cos5x^sin3√x

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Solución