# Thread: a curve is defined by y=x^2(x-2)^2

1. ## a curve is defined by y=x^2(x-2)^2

this is the questions: a curve is defined by y=x^2(x-2)^2.show that dy/dx=4x(x-1)(x-2)..

2. Probably easiest to do: product rule then factorise

Edit:

Just in case a picture helps...

... where

... the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x

Note that you can almost forget the chain rule for (x-2)^2 because the inner derivative is 1.

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