Answer to Question #274864 in Calculus for Kelfcake

Question

Differentiate the following functions.(use Chain Rules)

1. y=(5x² —2x + 1)—³

Answer 1

Let us differentiate the function

1. $y=(5x^2 -2x + 1)^{-3}$

It follows that

$y'=-3(5x^2 -2x + 1)^{-4}(5x^2 -2x + 1)'=-3(5x^2 -2x + 1)^{-4}(10x -2)$

$=-6(5x -1)(5x^2 -2x + 1)^{-4}.$