How do you use the chain rule to differentiate #y=(3x^4-7x^3+3x^2-5x)^3#?

1 Answer
Henry W.
Oct 9, 2016

#(dy)/(dx)=3(12x^3-21x^2+6x-5)(3x^4-7x^3+3x^2-5x)^2#

Explanation:

Chain rule: #(dy)/(dx)=(dy)/(du)*(du)/(dx)#

Let #u=3x^4-7x^3+3x^2-5x#,
then #(du)/(dx)=12x^3-21x^2+6x-5#

#y=u^3#, so #(dy)/(du)=3u^2=3(3x^4-7x^3+3x^2-5x)^2#

#:.(dy)/(dx)=(12x^3-21x^2+6x-5)*3(3x^4-7x^3+3x^2-5x)^2=3(12x^3-21x^2+6x-5)(3x^4-7x^3+3x^2-5x)^2#

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