How do you find the derivative of f(x) = x^2(x-2)^4f(x)=x2(x−2)4?

1 Answer
Hubert
May 28, 2015

f'(x)=(x^2)'(x-2)^4+x^2((x-2)^4)'=
=2x(x-2)^4+x^2*4(x-2)^3=
now just simplifying
=(x-2)^3[2x(x-2)+4x^2]=
=(6x^2-4x)(x-2)^3=6x(x-2/3)(x-2)^3
Rules used:
Product Rule: (f(x)*g(x))'=f'(x)*g(x)+f(x)g'(x)
Power Rule: (x^a)'=a*x^(a-1)
Chain Rule: [f(g(x))]'=f'(g(x))*g'(x)

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