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Derivada de:
Derivada de i*n*x
Derivada de 3^-x
Derivada de y=6x
Derivada de 25/x
Expresiones idénticas
y=(arctg(4x))^x^ dos
y es igual a (arctg(4x)) en el grado x al cuadrado
y es igual a (arctg(4x)) en el grado x en el grado dos
y=(arctg(4x))x2
y=arctg4xx2
y=(arctg(4x))^x²
y=(arctg(4x)) en el grado x en el grado 2
y=arctg4x^x^2

Derivada de la función/ arctg/ tg(4x)/ y=(arctg(4x))^x^2

Derivada de y=(arctg(4x))^x^2

Solución

Ha introducido [src]

           / 2\
           \x /
(atan(4*x))

\operatorname{atan}^{x^{2}}{\left(4 x \right)}

atan(4*x)^(x^2)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

           / 2\ /                                 2        \
           \x / |                              4*x         |
(atan(4*x))    *|2*x*log(atan(4*x)) + ---------------------|
                |                     /        2\          |
                \                     \1 + 16*x /*atan(4*x)/

\left(\frac{4 x^{2}}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + 2 x \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) \operatorname{atan}^{x^{2}}{\left(4 x \right)}

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Segunda derivada [src]

             / 2\ /                                             2               3                         2                                                  \
             \x / |   2 /         2*x                          \            64*x                       8*x                      8*x                          |
2*(atan(4*x))    *|2*x *|--------------------- + log(atan(4*x))|  - ---------------------- - ----------------------- + --------------------- + log(atan(4*x))|
                  |     |/        2\                           |               2                        2              /        2\                           |
                  |     \\1 + 16*x /*atan(4*x)                 /    /        2\              /        2\      2        \1 + 16*x /*atan(4*x)                 |
                  \                                                 \1 + 16*x / *atan(4*x)   \1 + 16*x / *atan (4*x)                                         /

2 \left(- \frac{64 x^{3}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + 2 x^{2} \left(\frac{2 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right)^{2} - \frac{8 x^{2}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} + \frac{8 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) \operatorname{atan}^{x^{2}}{\left(4 x \right)}

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Tercera derivada [src]

                  /                                                                                                                                                                                               /           2            4                                           2                         3        \\
                  |                                                                                                                                                                                               |      112*x       1024*x                12*x                    16*x                     192*x         ||
                  |                                                                                                                                                                                             2*|3 - --------- + ------------ - --------------------- + ----------------------- + ----------------------||
                  |                                                                                                                                                                                               |            2              2   /        2\                        2                         2          ||
             / 2\ |                                             3                                                /                                                       2                        3         \     |    1 + 16*x    /        2\    \1 + 16*x /*atan(4*x)   /        2\      2        /        2\           ||
             \x / |   3 /         2*x                          \        /         2*x                          \ |                           8*x                      8*x                     64*x          |     \                \1 + 16*x /                            \1 + 16*x / *atan (4*x)   \1 + 16*x / *atan(4*x)/|
4*(atan(4*x))    *|2*x *|--------------------- + log(atan(4*x))|  - 3*x*|--------------------- + log(atan(4*x))|*|-log(atan(4*x)) - --------------------- + ----------------------- + ----------------------| + -----------------------------------------------------------------------------------------------------------|
                  |     |/        2\                           |        |/        2\                           | |                  /        2\                        2                         2          |                                              /        2\                                                     |
                  |     \\1 + 16*x /*atan(4*x)                 /        \\1 + 16*x /*atan(4*x)                 / |                  \1 + 16*x /*atan(4*x)   /        2\      2        /        2\           |                                              \1 + 16*x /*atan(4*x)                                           |
                  \                                                                                              \                                          \1 + 16*x / *atan (4*x)   \1 + 16*x / *atan(4*x)/                                                                                                              /

4 \left(2 x^{3} \left(\frac{2 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right)^{3} - 3 x \left(\frac{2 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) \left(\frac{64 x^{3}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \frac{8 x^{2}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} - \frac{8 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) + \frac{2 \left(\frac{1024 x^{4}}{\left(16 x^{2} + 1\right)^{2}} + \frac{192 x^{3}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} - \frac{112 x^{2}}{16 x^{2} + 1} + \frac{16 x^{2}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} - \frac{12 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + 3\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right) \operatorname{atan}^{x^{2}}{\left(4 x \right)}

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Gráfico

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Expresiones idénticas

Derivada de y=(arctg(4x))^x^2

Gráfico:

Definida a trozos:

Solución