Question

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

Answer 1

`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)`