Question

Помогите пожалуйста найти производную функции в 4ом!!!

Answer 1

$y=ln \sqrt{ \frac{6x+1}{ x^{2} -2} } \\\\y'= \frac{1}{ \sqrt{ \frac{6x+1}{ x^{2} -2} } }*( \sqrt{ \frac{6x+1}{ x^{2} -2} })'= \frac{1}{ \sqrt{ \frac{6x+1}{ x^{2} -2} } } * \frac{1}{2 \sqrt{ \frac{6x+1}{ x^{2} -2} } }*( \frac{6x+1}{ x^{2} -2})'= \frac{1}{2* \frac{6x+1}{ x^{2} -2} } *$$\frac{(6x+1)'*( x^{2} -2)-(6x+1)( x^{2} -2)'}{( x^{2} -2) ^{2} } = \frac{ x^{2} -2}{2(6x+1)}* \frac{6( x^{2} -2)-2x(6x-1)}{( x^{2} -2) ^{2} }=$$\frac{6 x^{2} -12-12 x^{2} +2x}{2(6x+1)( x^{2} -2)} = \frac{-6 x^{2} +2x-12}{2(6x+1)( x^{2} -2)} =- \frac{3 x^{2} -x+6}{(6x+1)( x^{2} -2)}$