Question

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

Answer 1

`d/dx[(lnx)/(sinx)]=(sinx*1/x-lnxcosx)/(sin^2x)`

Explanation:

The quotient rule states that 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.

ie. `d/dx [(f(x))/(g(x))]=(g(x)*f'(x)-f(x)*g'(x))/([g(x)]^2)`

Applying this rule in this particular function gives the following result

`d/dx[(lnx)/(sinx)]=(sinx*1/x-lnxcosx)/(sin^2x)`