Question

How do you differentiate `f(x)=(e^x+x)(cotx+x)` using the product rule?

Answer 1

`[(e^x +1) * (cot x + x)] + [ (e^x +x) * (1 - csc^2x)]`

Explanation:

`d/dx e^x = e^x`

`d/dx x = 1`

`d/dx cot x = -csc^2x`

`d/dx x = 1`

According to product rule,
`f'(x) = [d/dx e^x + d/dx x] * (cot x + x) + (e^x +x) * [d/dx cot x + d/dx x]`

`= [(e^x +1) * (cot x + x)] + [ (e^x +x) * (1 - csc^2x)]`