Question

How do you differentiate `f(x)=(x)(x+7)(x-12)`?

Answer 1

I would use the Product Rule (actually one inside another one):
if you have: `f(x)=g(x)h(x)` you get:

`f'(x)=g'(x)h(x)+g(x)h'(x)`
considering that your `g(x)` is actually 2 functions!

So you get:
`f'(x)=[1*(x+7)+x*1]*(x-12)+x(x+7)*1=`
`=(2x+7)(x-12)+x^2+7x=`
`=2x^2-24x+7x-84+x^2+7x=`
`=3x^2-10x-84`

Alternatively you pre-multiply everything and derive:
`f(x)=(x^2+7x)(x-12)=`
`=x^3-12x^2+7x^2-84x=`
`=x^3-5x^2-84x` that derived gives the same.