Question

How do you find the derivative of `sin(x)/[1-cos(x)]`?

Answer 1

Use the quotient rule and algebraic simplification to obtain
`d/dx[sinx/(1-cosx)]=-1/(1-cosx)`

Explanation:

According to the quotient rule, the derivative of a quotient of 2 functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

Applying this to the given quotient and using normal rules for differentiation, we get :

`d/dx[sinx/(1-cosx)]=((1-cosx)*(cosx)-(sinx)*(sinx))/(1-cosx)^2`

`=(cosx-cos^2x-sin^2x)/((1-cosx)(1-cosx))`

`=-1/(1-cosx)`