Question

СРОЧНО ДАЮ 100б Найдите производную сложных функций

Answer 1

Ответ:

$\displaystyle h'(x) = \bigg(sin(x)+\frac{sin(x)}{cos^(x)} \bigg)*e^{sin(x)*tg(x)}$

Объяснение:

$\displaystyle h(x) = e^{sin(x)*tg(x)}\\\\\\h'(x) = \bigg(e^{sin(x)*tg(x)}\bigg)'*\bigg(sin(x)*tg(x)\bigg)'\\\\\\ \bigg(e^{sin(x)*tg(x)}\bigg)' = e^{sin(x)*tg(x)}\\\\\\(uv)'=u'v+uv'\\\\\bigg(sin(x)*tg(x)\bigg)'= (sin(x))'*tg(x)+sin(x)*(tg(x))'=\\\\\\=cos(x)*tg(x)+sin(x)*\frac{1}{cos^2(x)}$

ответ

$\displaystyle h'(x) = \bigg(sin(x)+\frac{sin(x)}{cos^(x)} \bigg)*e^{sin(x)*tg(x)}$