Question

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

Answer 1

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

Explanation:

let `f=x` and `g=1-sinx`

`f'=1,g'=-cosx`

Quotient Rule:
`f'(x)=(gf'-fg')/g^2`

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

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