Question

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

Answer 1

f`(x)=[6*√(x²+1)-6x*2x/2√(x²+1)]/(x²+1)=(6x²+6-6x²)/√(x²+1)³=6/√(x²+1)³
f(√3)=6√3/√(3+1)=6√3/2=3√3

Answer 2

$f(x)= \frac{6x}{ \sqrt{x^2+1} } \\ \\ f'(x)= \frac{(6x)'* \sqrt{x^2+1}-6x*( \sqrt{x^2+1} )' }{( \sqrt{x^2+1})^2 }= \\ \\ \frac{6 \sqrt{x^2+1}-6x* \frac{1}{2 \sqrt{x^2+1} }*2x }{ (\sqrt{x^2+1})^2 } = \frac{6(x^2+1)-6x^2}{(\sqrt{x^2+1})^2* \sqrt{x^+1} } = \frac{6}{ (x^2+1)^{ \frac{3}{2} } } \\ \\ f( \sqrt{3} )= \frac{6 \sqrt{3} }{ \sqrt{3+1} } =3 \sqrt{3}$