Solución detallada
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Sustituimos .
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Luego se aplica una cadena de reglas. Multiplicamos por :
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Sustituimos .
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Luego se aplica una cadena de reglas. Multiplicamos por :
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La derivada del seno es igual al coseno:
Como resultado de la secuencia de reglas:
Como resultado de la secuencia de reglas:
Respuesta:
/ sin(x)\
sin(x) \2 /
2 *(cos(3)) *(pi*I + log(-cos(3)))*cos(x)*log(2)
$$2^{\sin{\left(x \right)}} \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \log{\left(2 \right)} \cos^{2^{\sin{\left(x \right)}}}{\left(3 \right)} \cos{\left(x \right)}$$
/ sin(x)\
sin(x) \2 / / 2 sin(x) 2 \
2 *(cos(3)) *(pi*I + log(-cos(3)))*\-sin(x) + cos (x)*log(2) + 2 *cos (x)*(pi*I + log(-cos(3)))*log(2)/*log(2)
$$2^{\sin{\left(x \right)}} \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(2^{\sin{\left(x \right)}} \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \log{\left(2 \right)} \cos^{2}{\left(x \right)} - \sin{\left(x \right)} + \log{\left(2 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(2 \right)} \cos^{2^{\sin{\left(x \right)}}}{\left(3 \right)}$$
/ sin(x)\
sin(x) \2 / / 2 2 2*sin(x) 2 2 2 sin(x) sin(x) 2 2 \
2 *(cos(3)) *(pi*I + log(-cos(3)))*\-1 + cos (x)*log (2) - 3*log(2)*sin(x) + 2 *(pi*I + log(-cos(3))) *cos (x)*log (2) - 3*2 *(pi*I + log(-cos(3)))*log(2)*sin(x) + 3*2 *cos (x)*log (2)*(pi*I + log(-cos(3)))/*cos(x)*log(2)
$$2^{\sin{\left(x \right)}} \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(2^{2 \sin{\left(x \right)}} \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \log{\left(2 \right)}^{2} \cos^{2}{\left(x \right)} - 3 \cdot 2^{\sin{\left(x \right)}} \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \log{\left(2 \right)} \sin{\left(x \right)} + 3 \cdot 2^{\sin{\left(x \right)}} \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \log{\left(2 \right)}^{2} \cos^{2}{\left(x \right)} - 3 \log{\left(2 \right)} \sin{\left(x \right)} + \log{\left(2 \right)}^{2} \cos^{2}{\left(x \right)} - 1\right) \log{\left(2 \right)} \cos^{2^{\sin{\left(x \right)}}}{\left(3 \right)} \cos{\left(x \right)}$$