Question

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

Answer 1

`e^x(x^3-1)+3x^2e^x`

Explanation:

`frac{d}{dx}(e^x(x^3-1))`

applying product rule, `(fcdot g)^'=f^'cdot g+fcdot g^'`
`f=e^x,g=x^3-1`

`=frac{d}{dx}(e^x)(x^3-1)+frac{d}{dx}(x^3-1)e^x`

we know,
`frac{d}{dx}(e^x)=e^x`
and,
`frac{d}{dx}(x^3-1)=3x^2`

finally,
simplifying it,
`e^x(x^3-1)+3x^2e^x`