How to find the derivative using chain rule?

Question

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

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Answer 1 · 2017-09-01T07:43:24

#E#

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

we want#(dy)/(dx)#

we need the chain rule which is:

#(dy)/(dx)=(dy)/(du)(du)/(dx)#

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

#:.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#