Question

How do you differentiate `f(x)=(x-sinx)/(x^2-tanx)` using the quotient rule?

Answer 1

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

Explanation:

`"given "f(x)=(g(x))/(h(x))" then"`

`f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr"quotient rule"`

`g(x)=x-sinxrArrg'(x)=1-cosx`

`h(x)=x^2-tanxrArrh'(x)=2x-sec^2x`

`rArrf'(x)=((x^2-tanx)(1-cosx)-(x-sinx)(2x-sec^2x))/(x^2-tanx)^2`