Question

Найти производную функции :
1) у=∛х+2х³
2) у=(2х+3)³

Answer 1

$y=sqrt[3]{x}+ 2x^3=x^{frac{1}{3}} + 2x^3\y'=dfrac{1}{3}x^{frac{1}{3}-1} + 2cdot3x^2=dfrac{1}{3}x^{-frac{2}{3}} +6x^2=dfrac{1}{3sqrt[3]{x^2} }+6x^2$

$y=(2x+3)^3\y'=3(2x+3)^2cdot(2x+3)'=3(2x+3)^2cdot2=6(2x+3)^2$