this is the questions: a curve is defined by y=x^2(x-2)^2.show that dy/dx=4x(x-1)(x-2)..
someone please help..
Probably easiest to do: product rule then factorise
Just in case a picture helps...
... 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.
Don't integrate - balloontegrate!
Draw balloons with LaTeX: http://www.ballooncalculus.org/asy/doc.html