Question

Найти производную y' данной функции
4(sin(x^5)*arctg(x^3))^7+4Sh(9arccos(x^3)+8arcctg(x^4))

Answer 1

Пошаговое объяснение:

$\frac{d}{d x}\left(4\left(\sin \left(x^{5}\right) \tan ^{-1}\left(x^{3}\right)\right)^{7}+4 \sinh \left(9 \cos ^{-1}\left(x^{3}\right)+8 \cot ^{-1}\left(x^{4}\right)\right)\right)=$

$140 x^{4} \sin ^{6}\left(x^{5}\right) \cos \left(x^{5}\right) \tan ^{-1}\left(x^{3}\right)^{7}+\frac{84 x^{2} \sin ^{7}\left(x^{5}\right) \tan ^{-1}\left(x^{3}\right)^{6}}{x^{6}+1}+$

$4\left(-\frac{32 x^{3}}{x^{8}+1}-\frac{27 x^{2}}{\sqrt{1-x^{6}}}\right) \cosh \left(9 \cos ^{-1}\left(x^{3}\right)+8 \cot ^{-1}\left(x^{4}\right)\right)$