Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
x*atan(7*x) // 7*x \ \
x *||--------- + atan(7*x)|*log(x) + atan(7*x)|
|| 2 | |
\\1 + 49*x / /
$$x^{x \operatorname{atan}{\left(7 x \right)}} \left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right)$$
/ / 2 \ \
| 7*x | 49*x | |
| --------- + atan(7*x) 14*|-1 + ---------|*log(x)|
| 2 2 | 2| |
x*atan(7*x) |// 7*x \ \ 7 1 + 49*x \ 1 + 49*x / |
x *|||--------- + atan(7*x)|*log(x) + atan(7*x)| + --------- + --------------------- - --------------------------|
||| 2 | | 2 x 2 |
\\\1 + 49*x / / 1 + 49*x 1 + 49*x /
$$x^{x \operatorname{atan}{\left(7 x \right)}} \left(\left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right)^{2} - \frac{14 \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right) \log{\left(x \right)}}{49 x^{2} + 1} + \frac{7}{49 x^{2} + 1} + \frac{\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}}{x}\right)$$
/ / / 2 \ \ / 2 \ / 2 \ \
| 7*x | 7*x | 49*x | | | 49*x | | 49*x | |
| --------- + atan(7*x) | --------- + atan(7*x) 14*|-1 + ---------|*log(x)| 28*|-1 + ---------| 2744*x*|-1 + ---------|*log(x)|
| 3 2 | 2 | 2| | | 2| | 2| |
x*atan(7*x) |// 7*x \ \ 1 + 49*x 686*x // 7*x \ \ | 7 1 + 49*x \ 1 + 49*x / | \ 1 + 49*x / \ 1 + 49*x / |
x *|||--------- + atan(7*x)|*log(x) + atan(7*x)| - --------------------- - ------------ + 3*||--------- + atan(7*x)|*log(x) + atan(7*x)|*|--------- + --------------------- - --------------------------| - ------------------- + ------------------------------|
||| 2 | | 2 2 || 2 | | | 2 x 2 | / 2\ 2 |
|\\1 + 49*x / / x / 2\ \\1 + 49*x / / \1 + 49*x 1 + 49*x / x*\1 + 49*x / / 2\ |
\ \1 + 49*x / \1 + 49*x / /
$$x^{x \operatorname{atan}{\left(7 x \right)}} \left(\frac{2744 x \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right) \log{\left(x \right)}}{\left(49 x^{2} + 1\right)^{2}} - \frac{686 x}{\left(49 x^{2} + 1\right)^{2}} + \left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right)^{3} + 3 \left(\left(\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}\right) \log{\left(x \right)} + \operatorname{atan}{\left(7 x \right)}\right) \left(- \frac{14 \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right) \log{\left(x \right)}}{49 x^{2} + 1} + \frac{7}{49 x^{2} + 1} + \frac{\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}}{x}\right) - \frac{28 \left(\frac{49 x^{2}}{49 x^{2} + 1} - 1\right)}{x \left(49 x^{2} + 1\right)} - \frac{\frac{7 x}{49 x^{2} + 1} + \operatorname{atan}{\left(7 x \right)}}{x^{2}}\right)$$