Question

How do you find the derivative of `f(x)=(x^5+6x^2-1)(1-3x)^2`?

Answer 1

I would use the Product and Chain Rule (to deal with the `()^2`):
`f'(x)=(5x^4+12x)(1-3x)^2+(x^5+6x^2-1)2(1-3x)(-3)=`
`=(1-3x)[(5x^4+12x)(1-3x)-6(x^5+6x^2-1)]=`
`=(1-3x)[-21x^5+5x^4-72x^2+12x+6]`