Question

Найти производную функции
$y=( 2x^{2} +1)( sqrt{7-3x})$

Answer 1

$y'=(2 x^{2} +1)'( sqrt{7-3x})+(2 x^{2} +1)(sqrt{7-3x})'=\ =4xsqrt{7-3x}+(2 x^{2} +1) frac{1}{2sqrt{7-3x}}*(-3)=\ = frac{4xsqrt{7-3x}*2sqrt{7-3x}-3(2 x^{2} +1)}{2sqrt{7-3x}}=\ = frac{8x(7-3x)-6 x^{2} -3}{2sqrt{7-3x}}=frac{56x-24 x^{2} -6 x^{2} -3}{2sqrt{7-3x}}=\ = frac{-30 x^{2} +56x-3}{2sqrt{7-3x}}$