How to find the derivative using chain rule?

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Can someone please explain to me how to do question 2? Thanks.

1 Answer
Sep 1, 2017

EE

Explanation:

Given y=(3x^2-x)^2y=(3x2x)2

we want(dy)/(dx)dydx

we need the chain rule which is:

(dy)/(dx)=(dy)/(du)(du)/(dx)dydx=dydududx

let" "u=3x^2-x=>color(blue)((du)/(dx)=6x-1) u=3x2xdudx=6x1

:.y=u^2=>color(red)((dy)/(du)=2u)

(dy)/(dx)=color(red)((dy)/(du))color(blue)((du)/(dx))

(dy)/(dx)=color(red)(2u)color(blue)((6x-1))

substitute back for u

(dy)/(dx)=2(3x^2-x)(6x-1)

we need to take out common factor from the first bracket

=2x(3x-1)(6x-1)

answer E