Question

What is the derivative of `f(x) = x^2(x-2)^4`?

Answer 1

`(df)/(dx)=2x(x-2)^3(3x-2)`

Explanation:

Product rule states that if `f(x)=g(x)*h(x)`

`(df)/(dx) = g(x)xx(dh)/(dx) + h(x)xx(dg)/(dx)`

Here `g(x)=x^2` and `h(x)=(x-2)^4`

Hence, `(df)/(dx)=x^2xx4(x-2)^3+(x-2)^4xx2x`

= `2x(x-2)^3{2x+(x-2)}`

= `2x(x-2)^3(3x-2)`