Question

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

Answer 1

`f'(x)=(lnx-x)(1/x+cosx)+(lnx+sinx)(1/x-1)`

Explanation:

Know that: `{(d/dx[lnx]=1/x),(d/dx[sinx]=cosx):}`

According to the product rule:

`f'(x)=(lnx-x)d/dx[lnx+sinx]+(lnx+sinx)d/dx[lnx-x]`

`=>(lnx-x)(1/x+cosx)+(lnx+sinx)(1/x-1)`