Question

How do you differentiate `f(x) = (-11x) / (sin(x)+cos(x))`?

Answer 1

`f'(x)=((11sinx)(x+1)+(11cosx)(1-x))/(sinx+cosx)^2`

Explanation:

`f(x)=(-11x)/(sinx+cosx)`

`f'(x)=((cosx-sinx)(-11x)-(sinx+cosx)times(-11))/(sinx+cosx)^2`

`f'(x)=(-11xcosx+11xsinx+11sinx+11cosx)/(sinx+cosx)^2`

`f'(x)=((11sinx)(x+1)+(11cosx)(1-x))/(sinx+cosx)^2`

Remember:
IF `f(x)=u/v`
THEN `f'(x)=(v'u-vu')/v^2`