Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
2*x + 3 / 2*x + 3 \
atan (x)*|2*log(atan(x)) + ----------------|
| / 2\ |
\ \1 + x /*atan(x)/
$$\left(\frac{2 x + 3}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + 2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right) \operatorname{atan}^{2 x + 3}{\left(x \right)}$$
/ 3 + 2*x 2*x*(3 + 2*x)\
| -4 + ---------------- + -------------|
| 2 / 2\ 2 |
3 + 2*x |/ 3 + 2*x \ \1 + x /*atan(x) 1 + x |
atan (x)*||2*log(atan(x)) + ----------------| - -------------------------------------|
|| / 2\ | / 2\ |
\\ \1 + x /*atan(x)/ \1 + x /*atan(x) /
$$\left(\left(\frac{2 x + 3}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + 2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right)^{2} - \frac{\frac{2 x \left(2 x + 3\right)}{x^{2} + 1} + \frac{2 x + 3}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 4}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}\right) \operatorname{atan}^{2 x + 3}{\left(x \right)}$$
/ / 2 \ \
| | 3 3 + 2*x 4*x *(3 + 2*x) 3*x*(3 + 2*x) | / 3 + 2*x \ / 3 + 2*x 2*x*(3 + 2*x)\|
| 2*|-3 - 8*x - ------- + ----------------- + -------------- + ----------------| 3*|2*log(atan(x)) + ----------------|*|-4 + ---------------- + -------------||
| 3 | atan(x) / 2\ 2 2 / 2\ | | / 2\ | | / 2\ 2 ||
3 + 2*x |/ 3 + 2*x \ \ \1 + x /*atan (x) 1 + x \1 + x /*atan(x)/ \ \1 + x /*atan(x)/ \ \1 + x /*atan(x) 1 + x /|
atan (x)*||2*log(atan(x)) + ----------------| + ------------------------------------------------------------------------------ - -----------------------------------------------------------------------------|
|| / 2\ | 2 / 2\ |
|\ \1 + x /*atan(x)/ / 2\ \1 + x /*atan(x) |
\ \1 + x / *atan(x) /
$$\left(\left(\frac{2 x + 3}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + 2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right)^{3} - \frac{3 \left(\frac{2 x + 3}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + 2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right) \left(\frac{2 x \left(2 x + 3\right)}{x^{2} + 1} + \frac{2 x + 3}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 4\right)}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{2 \left(\frac{4 x^{2} \left(2 x + 3\right)}{x^{2} + 1} + \frac{3 x \left(2 x + 3\right)}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - 8 x + \frac{2 x + 3}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left(x \right)}} - 3 - \frac{3}{\operatorname{atan}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}}\right) \operatorname{atan}^{2 x + 3}{\left(x \right)}$$