Question

Помогите решить две производные

Answer 1

1.
$y = {x}^{4} sqrt{ {x}^{7} } sqrt[3]{ {x}^{5} } = {x}^{4} {x}^{ frac{7}{2} } {x}^{ frac{5}{3} } = {x}^{4 + frac{7}{2} + frac{5}{3}} = {x}^{frac{24 + 21 + 10}{6}} = {x}^{frac{55}{6}} \ frac{dy}{dx} = frac{55}{6} {x}^{frac{49}{6}}$

2.
$f(x)=arcctg(frac{2x}{1+x^2}) \ f'(x)= -frac{2(1+x^2) - 4x^2}{(1+x^2)^2} times frac{1}{1+(frac{2x}{1+x^2})^2}$