Question 260676
*[Tex \LARGE y=(x-1)^3(x^2-2)^2] ... Start with the given equation



*[Tex \LARGE y^{\prime}=\frac{d}{dx}\left((x-1)^3(x^2-2)^2\right)] ... Derive both sides with respect to x.



*[Tex \LARGE y^{\prime}=\frac{d}{dx}\left((x-1)^3\right)(x^2-2)^2+(x-1)^3\frac{d}{dx}\left((x^2-2)^2\right)] ... Use the product rule.



*[Tex \LARGE y^{\prime}=3(x-1)^2(x^2-2)^2+4x(x-1)^3(x^2-2)] ... Use the chain rule.


Here's <a href="http://www.wolframalpha.com/input/?i=%28x-1%29^3*%28x^2-2%29^2">confirmation</a> of the answer.