Derivada de y=x^arctan7x

Ha introducido [src]

 atan(7*x)
x

x^{\operatorname{atan}{\left(7 x \right)}}

x^atan(7*x)

Solución detallada

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Perola derivada

$\left(\log{\left(\operatorname{atan}{\left(7 x \right)} \right)} + 1\right) \operatorname{atan}^{\operatorname{atan}{\left(7 x \right)}}{\left(7 x \right)}$

Respuesta:

$\left(\log{\left(\operatorname{atan}{\left(7 x \right)} \right)} + 1\right) \operatorname{atan}^{\operatorname{atan}{\left(7 x \right)}}{\left(7 x \right)}$

Gráfica

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Primera derivada [src]

 atan(7*x) /atan(7*x)    7*log(x)\
x         *|--------- + ---------|
           |    x               2|
           \            1 + 49*x /

x^{\operatorname{atan}{\left(7 x \right)}} \left(\frac{7 \log{\left(x \right)}}{49 x^{2} + 1} + \frac{\operatorname{atan}{\left(7 x \right)}}{x}\right)

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Segunda derivada [src]

           /                       2                                           \
 atan(7*x) |/atan(7*x)    7*log(x)\    atan(7*x)         14        686*x*log(x)|
x         *||--------- + ---------|  - --------- + ------------- - ------------|
           ||    x               2|         2        /        2\              2|
           |\            1 + 49*x /        x       x*\1 + 49*x /   /        2\ |
           \                                                       \1 + 49*x / /

x^{\operatorname{atan}{\left(7 x \right)}} \left(- \frac{686 x \log{\left(x \right)}}{\left(49 x^{2} + 1\right)^{2}} + \left(\frac{7 \log{\left(x \right)}}{49 x^{2} + 1} + \frac{\operatorname{atan}{\left(7 x \right)}}{x}\right)^{2} + \frac{14}{x \left(49 x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(7 x \right)}}{x^{2}}\right)

Simplificar

Tercera derivada [src]

           /                       3                                                                                                                                               2       \
 atan(7*x) |/atan(7*x)    7*log(x)\        2058        686*log(x)          21           /atan(7*x)    7*log(x)\ /atan(7*x)         14        686*x*log(x)\   2*atan(7*x)   134456*x *log(x)|
x         *||--------- + ---------|  - ------------ - ------------ - -------------- - 3*|--------- + ---------|*|--------- - ------------- + ------------| + ----------- + ----------------|
           ||    x               2|               2              2    2 /        2\     |    x               2| |     2        /        2\              2|         3                    3  |
           |\            1 + 49*x /    /        2\    /        2\    x *\1 + 49*x /     \            1 + 49*x / |    x       x*\1 + 49*x /   /        2\ |        x          /        2\   |
           \                           \1 + 49*x /    \1 + 49*x /                                               \                            \1 + 49*x / /                   \1 + 49*x /   /

x^{\operatorname{atan}{\left(7 x \right)}} \left(\frac{134456 x^{2} \log{\left(x \right)}}{\left(49 x^{2} + 1\right)^{3}} + \left(\frac{7 \log{\left(x \right)}}{49 x^{2} + 1} + \frac{\operatorname{atan}{\left(7 x \right)}}{x}\right)^{3} - 3 \left(\frac{7 \log{\left(x \right)}}{49 x^{2} + 1} + \frac{\operatorname{atan}{\left(7 x \right)}}{x}\right) \left(\frac{686 x \log{\left(x \right)}}{\left(49 x^{2} + 1\right)^{2}} - \frac{14}{x \left(49 x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(7 x \right)}}{x^{2}}\right) - \frac{686 \log{\left(x \right)}}{\left(49 x^{2} + 1\right)^{2}} - \frac{2058}{\left(49 x^{2} + 1\right)^{2}} - \frac{21}{x^{2} \left(49 x^{2} + 1\right)} + \frac{2 \operatorname{atan}{\left(7 x \right)}}{x^{3}}\right)

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Gráfico

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Expresiones idénticas

Derivada de y=x^arctan7x

Gráfico:

Definida a trozos:

Solución