Question

How do you differentiate `(x+1/x)tanx`?

Answer 1

`(1-1/x^2)tanx+sec^2x(x+1/x)`

Explanation:

Using product rule
`d/dx(f(x)g(x))=f'(x)g(x)+f(x)g'(x)`
where `f(x)=x+1/x` and `g(x)= tanx`

`(1+(-1)x^(-2))tanx+(x+1/x)sec^2x`
`(1-1/x^2)tanx+(x+1/x)sec^2x`