Question

Найти f'(0где f(x) =x/корень из 1-x2

Answer 1

$f(x)=frac{x}{sqrt{1-x^2}}\\f'(x)=frac{sqrt{1-x^2}+frac{x*2x}{2sqrt{1-x^2}}}{1-x^2}=frac{frac{1-x^2+x^2}{sqrt{1-x^2}}}{1-x^2}=frac{1}{(1-x^2)sqrt{1-x^2}}=(1-x^2)^{-frac{3}2}\\f'(0)=(1)^{-frac{3}2}=1$