Solución detallada
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La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Entonces, como resultado:
Respuesta:
cot(2*x) /cot(2*x) / 2 \ \
-x *|-------- + \-2 - 2*cot (2*x)/*log(x)|
\ x /
$$- x^{\cot{\left(2 x \right)}} \left(\left(- 2 \cot^{2}{\left(2 x \right)} - 2\right) \log{\left(x \right)} + \frac{\cot{\left(2 x \right)}}{x}\right)$$
/ 2 / 2 \ \
cot(2*x) |/ cot(2*x) / 2 \ \ cot(2*x) 4*\1 + cot (2*x)/ / 2 \ |
-x *||- -------- + 2*\1 + cot (2*x)/*log(x)| - -------- - ----------------- + 8*\1 + cot (2*x)/*cot(2*x)*log(x)|
|\ x / 2 x |
\ x /
$$- x^{\cot{\left(2 x \right)}} \left(\left(2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(2 x \right)}}{x}\right)^{2} + 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} \cot{\left(2 x \right)} - \frac{4 \left(\cot^{2}{\left(2 x \right)} + 1\right)}{x} - \frac{\cot{\left(2 x \right)}}{x^{2}}\right)$$
/ 3 2 / / 2 \ \ / 2 \ / 2 \ \
cot(2*x) | / cot(2*x) / 2 \ \ / 2 \ 2*cot(2*x) / cot(2*x) / 2 \ \ |cot(2*x) 4*\1 + cot (2*x)/ / 2 \ | 6*\1 + cot (2*x)/ 2 / 2 \ 24*\1 + cot (2*x)/*cot(2*x)|
-x *|- |- -------- + 2*\1 + cot (2*x)/*log(x)| - 16*\1 + cot (2*x)/ *log(x) + ---------- + 3*|- -------- + 2*\1 + cot (2*x)/*log(x)|*|-------- + ----------------- - 8*\1 + cot (2*x)/*cot(2*x)*log(x)| + ----------------- - 32*cot (2*x)*\1 + cot (2*x)/*log(x) + ---------------------------|
| \ x / 3 \ x / | 2 x | 2 x |
\ x \ x / x /
$$- x^{\cot{\left(2 x \right)}} \left(- \left(2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(2 x \right)}}{x}\right)^{3} + 3 \left(2 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(2 x \right)}}{x}\right) \left(- 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} \cot{\left(2 x \right)} + \frac{4 \left(\cot^{2}{\left(2 x \right)} + 1\right)}{x} + \frac{\cot{\left(2 x \right)}}{x^{2}}\right) - 16 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x \right)} - 32 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} \cot^{2}{\left(2 x \right)} + \frac{24 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)}}{x} + \frac{6 \left(\cot^{2}{\left(2 x \right)} + 1\right)}{x^{2}} + \frac{2 \cot{\left(2 x \right)}}{x^{3}}\right)$$