Question

How do you differentiate `f(x)=(x-sinx)/(x-1)` using the quotient rule?

Answer 1

`f'(x)=(cosx(1-x)-1+sinx)/(x-1)^2`

Explanation:

According to quotient rule for `f(x)=(p(x))/(q(x))`

`f'(x)=(q(x)p'(x)-p(x)q'(x))/(q(x))^2`

Hence, for `f(x)=(x-sinx)/(x-1)`

`f'(x)=((x-1)(1-cosx)-(x-sinx)*1)/(x-1)^2`

= `(x-xcosx-1+cosx-x+sinx)/(x-1)^2`

= `(cosx(1-x)-1+sinx)/(x-1)^2`