Question

How do you differentiate `f(x)= e^(3x) * (5x^2-x+1)^12` using the product rule?

Answer 1

`f'(x)=12e^(3x)(10x-1)(5x^2-x+1)^11+3e^(3x)(5x^2-x+1)^12`

Explanation:

`f=e^(3x), g=(5x^2-x+1)^12`
`f'=e^(3x) * 3=3e^(3x), g'=12(5x^2-x+1)^11 *(10x-1)`
`f'(x)=fg'+gf'`
`f'(x)=12e^(3x)(10x-1)(5x^2-x+1)^11+3e^(3x)(5x^2-x+1)^12`