Question

Найти производную функции:
y=2*5^(-x)*ln²(5x+√x)
y'=?

Answer 1

$y=2* 5^{-x}* ln^{2}(5x+sqrt{x}) \ y'=5^{-x}* 2ln^{2}(5x+sqrt{x})= 5^{-x} ln5*2ln^{2}(5x+sqrt{x})+frac{5^{-x}}{(5x+sqrt{x})^{2}}=$$5^{-x}*( ln5*2ln^{2}(5x+sqrt{x})+frac{1}{(5x+sqrt{x})^{2}})$