Question

How do you differentiate `f(x)=(e^x-3lnx)(tanx+x^2)` using the product rule?

Answer 1

`f'(x)=(e^x-3/x)*(tan(x)+x^2)+(e^x-3ln(x))(tan^2(x)+2x+1)`

Explanation:

Using the product rule

`(uv)'=u'v+uv'`
We get
`u=e^x-3ln(x)`
so
`u'=e^x-3/x`

`v=tan(x)+x^2`
so

`v'=tan^2(x)+1+2x`