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(2*(x + 100)) /sin(2*(x + 100)) \
x *|---------------- + 2*cos(2*(x + 100))*log(x)|
\ x /
$$x^{\sin{\left(2 \left(x + 100\right) \right)}} \left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right)$$
/ 2 \
sin(2*(100 + x)) |/sin(2*(100 + x)) \ sin(2*(100 + x)) 4*cos(2*(100 + x))|
x *||---------------- + 2*cos(2*(100 + x))*log(x)| - ---------------- - 4*log(x)*sin(2*(100 + x)) + ------------------|
|\ x / 2 x |
\ x /
$$x^{\sin{\left(2 \left(x + 100\right) \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right)^{2} - 4 \log{\left(x \right)} \sin{\left(2 \left(x + 100\right) \right)} + \frac{4 \cos{\left(2 \left(x + 100\right) \right)}}{x} - \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x^{2}}\right)$$
/ 3 \
sin(2*(100 + x)) |/sin(2*(100 + x)) \ 12*sin(2*(100 + x)) 6*cos(2*(100 + x)) /sin(2*(100 + x)) \ /sin(2*(100 + x)) 4*cos(2*(100 + x)) \ 2*sin(2*(100 + x))|
x *||---------------- + 2*cos(2*(100 + x))*log(x)| - ------------------- - 8*cos(2*(100 + x))*log(x) - ------------------ - 3*|---------------- + 2*cos(2*(100 + x))*log(x)|*|---------------- - ------------------ + 4*log(x)*sin(2*(100 + x))| + ------------------|
|\ x / x 2 \ x / | 2 x | 3 |
\ x \ x / x /
$$x^{\sin{\left(2 \left(x + 100\right) \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right)^{3} - 3 \left(2 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(2 \left(x + 100\right) \right)} - \frac{4 \cos{\left(2 \left(x + 100\right) \right)}}{x} + \frac{\sin{\left(2 \left(x + 100\right) \right)}}{x^{2}}\right) - 8 \log{\left(x \right)} \cos{\left(2 \left(x + 100\right) \right)} - \frac{12 \sin{\left(2 \left(x + 100\right) \right)}}{x} - \frac{6 \cos{\left(2 \left(x + 100\right) \right)}}{x^{2}} + \frac{2 \sin{\left(2 \left(x + 100\right) \right)}}{x^{3}}\right)$$