Question

Вычислить производную y=cos^3 (sqrt x)

Answer 1

$y'=(cos^3 sqrt{x})' = 3(cos^2 sqrt{x})*(cos sqrt{x})' = \ \ = 3(cos^2 sqrt{x})*(-sin sqrt{x})*( sqrt{x} )'= 3(cos^2 sqrt{x})*(-sin sqrt{x})*( frac{1}{2 sqrt{x}})= \ \ = - frac{3}{2 sqrt{x}}(cos^2 sqrt{x})*(sin sqrt{x})$