Question

Помогите найти производную:
f(x)= 6x/√x^2+1; f(√3)

Answer 1

$f(x)=\frac{6x}{\sqrt{x^2+1}}\\\\f'(x)=\frac{6\cdot \sqrt{x^2+1}-6x\cdot \frac{2x}{2\sqrt{x^2+1}}}{x^2+1}=\frac{6\cdot (x^2+1)-6x^2}{(x^2+1)\sqrt{x^2+1}}=\frac{6}{\sqrt{(x^2+1)^3}} \\\\f'(\sqrt3)= \frac{6}{\sqrt{4^3}}=\frac{6}{2^3}=\frac{6}{8}=\frac{3}{4}=0,75$