Question

помогите пожалуйста.....

Answer 1

$f(x)=\frac{x}{\sqrt{x^2+1}}\\\\\\f'(x)=\frac{\sqrt{x^2+1}-x\cdot \frac{2x}{2\sqrt{x^2+1}}}{x^2+1}=\frac{x^2+1-x^2}{\sqrt{x^2+1}\cdot (x^2+1)}=\frac{1}{\sqrt{(x^2+1)^3}}=(x^2+1)^{-\frac{3}{2}}\\\\\\f''(x)=-\frac{3}{2}\cdot (x^2+1)^{-\frac{5}{2}}\cdot 2x}=-\frac{3x}{(x^2+1)^{\frac{5}{2}}}=-\frac{3x}{\sqrt{(x^2+1)^5}}\\\\\\f''(0)=-\frac{0}{1}=0$