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

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Answer 1 · 2016-04-06T11:09:20

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

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

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

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

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