Question

How do you differentiate #f(x)=x / cot (x) + 3# using the quotient rule?

Answer 1

I'm assuming


`f(x)=\frac x{\cot x+3}`

By the quotient rule, the derivative
`f'(x)` is


`((\cot x+3)(x)'-x(\cot x+3)')/((\cot x+3)^2)=((\cot x+3)(1)-x(-\csc^2x))/((\cot x+3)^2)=(x\csc^2x+\cot x+3)/((\cot x+3)^2)`