Question

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

Answer 1

The product rule `(uv)'=uv'+vu'` where `u` and `v` are functions of `x` Our answer would be `f'(x) = (x-3ln(x))(sec^2(x) + 2)+(tan(x)+2x)(1-3/x)`

Explanation:

To differentiate
`f(x) = (x-3ln(x))(tan(x)+2x)`
`f'(x) = (x-3ln(x))d/dx(tan(x)+2x) + (tan(x)+2x)d/dx(x-3ln(x))`
`f'(x) = (x-3ln(x)){d/dx(tan(x) + d/dx(2x)} + (tan(x)+2x){d/dx(x) - d/dx(3ln(x))}`

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