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:
/ 4 / 5\ \
x - 3/ 5\ |35*x *(x - 3)*cos\7*x / / / 5\\|
sin \7*x /*|----------------------- + log\sin\7*x //|
| / 5\ |
\ sin\7*x / /
$$\left(\frac{35 x^{4} \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} + \log{\left(\sin{\left(7 x^{5} \right)} \right)}\right) \sin^{x - 3}{\left(7 x^{5} \right)}$$
/ 2 \
|/ 4 / 5\ \ / / 5\ / 5\ 5 2/ 5\ \|
-3 + x/ 5\ ||35*x *(-3 + x)*cos\7*x / / / 5\\| 3 | 5 4*(-3 + x)*cos\7*x / 2*x*cos\7*x / 35*x *cos \7*x /*(-3 + x)||
sin \7*x /*||------------------------ + log\sin\7*x //| - 35*x *|35*x *(-3 + x) - -------------------- - ------------- + -------------------------||
|| / 5\ | | / 5\ / 5\ 2/ 5\ ||
\\ sin\7*x / / \ sin\7*x / sin\7*x / sin \7*x / //
$$\left(- 35 x^{3} \left(35 x^{5} \left(x - 3\right) + \frac{35 x^{5} \left(x - 3\right) \cos^{2}{\left(7 x^{5} \right)}}{\sin^{2}{\left(7 x^{5} \right)}} - \frac{2 x \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} - \frac{4 \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}}\right) + \left(\frac{35 x^{4} \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} + \log{\left(\sin{\left(7 x^{5} \right)} \right)}\right)^{2}\right) \sin^{x - 3}{\left(7 x^{5} \right)}$$
/ 3 \
|/ 4 / 5\ \ / 6 2/ 5\ / 5\ / 5\ 5 2/ 5\ 10 3/ 5\ 10 / 5\\ / 4 / 5\ \ / / 5\ / 5\ 5 2/ 5\ \|
-3 + x/ 5\ ||35*x *(-3 + x)*cos\7*x / / / 5\\| 2 | 6 5 105*x *cos \7*x / 12*x*cos\7*x / 12*(-3 + x)*cos\7*x / 420*x *cos \7*x /*(-3 + x) 2450*x *cos \7*x /*(-3 + x) 2450*x *(-3 + x)*cos\7*x /| 3 |35*x *(-3 + x)*cos\7*x / / / 5\\| | 5 4*(-3 + x)*cos\7*x / 2*x*cos\7*x / 35*x *cos \7*x /*(-3 + x)||
sin \7*x /*||------------------------ + log\sin\7*x //| + 35*x *|- 105*x - 420*x *(-3 + x) - ----------------- + -------------- + --------------------- - -------------------------- + ---------------------------- + ---------------------------| - 105*x *|------------------------ + log\sin\7*x //|*|35*x *(-3 + x) - -------------------- - ------------- + -------------------------||
|| / 5\ | | 2/ 5\ / 5\ / 5\ 2/ 5\ 3/ 5\ / 5\ | | / 5\ | | / 5\ / 5\ 2/ 5\ ||
\\ sin\7*x / / \ sin \7*x / sin\7*x / sin\7*x / sin \7*x / sin \7*x / sin\7*x / / \ sin\7*x / / \ sin\7*x / sin\7*x / sin \7*x / //
$$\left(- 105 x^{3} \left(\frac{35 x^{4} \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} + \log{\left(\sin{\left(7 x^{5} \right)} \right)}\right) \left(35 x^{5} \left(x - 3\right) + \frac{35 x^{5} \left(x - 3\right) \cos^{2}{\left(7 x^{5} \right)}}{\sin^{2}{\left(7 x^{5} \right)}} - \frac{2 x \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} - \frac{4 \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}}\right) + 35 x^{2} \left(\frac{2450 x^{10} \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} + \frac{2450 x^{10} \left(x - 3\right) \cos^{3}{\left(7 x^{5} \right)}}{\sin^{3}{\left(7 x^{5} \right)}} - 105 x^{6} - \frac{105 x^{6} \cos^{2}{\left(7 x^{5} \right)}}{\sin^{2}{\left(7 x^{5} \right)}} - 420 x^{5} \left(x - 3\right) - \frac{420 x^{5} \left(x - 3\right) \cos^{2}{\left(7 x^{5} \right)}}{\sin^{2}{\left(7 x^{5} \right)}} + \frac{12 x \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} + \frac{12 \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}}\right) + \left(\frac{35 x^{4} \left(x - 3\right) \cos{\left(7 x^{5} \right)}}{\sin{\left(7 x^{5} \right)}} + \log{\left(\sin{\left(7 x^{5} \right)} \right)}\right)^{3}\right) \sin^{x - 3}{\left(7 x^{5} \right)}$$