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:
sin(pi*x) + 1 /sin(pi*x) + 1 \
x *|------------- + pi*cos(pi*x)*log(x)|
\ x /
$$x^{\sin{\left(\pi x \right)} + 1} \left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{x}\right)$$
/ 2 \
1 + sin(pi*x) |/1 + sin(pi*x) \ 1 + sin(pi*x) 2 2*pi*cos(pi*x)|
x *||------------- + pi*cos(pi*x)*log(x)| - ------------- - pi *log(x)*sin(pi*x) + --------------|
|\ x / 2 x |
\ x /
$$x^{\sin{\left(\pi x \right)} + 1} \left(\left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{x}\right)^{2} - \pi^{2} \log{\left(x \right)} \sin{\left(\pi x \right)} + \frac{2 \pi \cos{\left(\pi x \right)}}{x} - \frac{\sin{\left(\pi x \right)} + 1}{x^{2}}\right)$$
/ 3 2 \
1 + sin(pi*x) |/1 + sin(pi*x) \ /1 + sin(pi*x) \ /1 + sin(pi*x) 2 2*pi*cos(pi*x)\ 2*(1 + sin(pi*x)) 3 3*pi*cos(pi*x) 3*pi *sin(pi*x)|
x *||------------- + pi*cos(pi*x)*log(x)| - 3*|------------- + pi*cos(pi*x)*log(x)|*|------------- + pi *log(x)*sin(pi*x) - --------------| + ----------------- - pi *cos(pi*x)*log(x) - -------------- - ---------------|
|\ x / \ x / | 2 x | 3 2 x |
\ \ x / x x /
$$x^{\sin{\left(\pi x \right)} + 1} \left(\left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{x}\right)^{3} - 3 \left(\pi \log{\left(x \right)} \cos{\left(\pi x \right)} + \frac{\sin{\left(\pi x \right)} + 1}{x}\right) \left(\pi^{2} \log{\left(x \right)} \sin{\left(\pi x \right)} - \frac{2 \pi \cos{\left(\pi x \right)}}{x} + \frac{\sin{\left(\pi x \right)} + 1}{x^{2}}\right) - \pi^{3} \log{\left(x \right)} \cos{\left(\pi x \right)} - \frac{3 \pi^{2} \sin{\left(\pi x \right)}}{x} - \frac{3 \pi \cos{\left(\pi x \right)}}{x^{2}} + \frac{2 \left(\sin{\left(\pi x \right)} + 1\right)}{x^{3}}\right)$$