Question

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

Answer 1

I'm assuming

$f(x)=\dfrac x{\cot x+3}$

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

$\dfrac{(\cot x+3)(x)'-x(\cot x+3)'}{(\cot x+3)^2}=\dfrac{(\cot x+3)(1)-x(-\csc^2x)}{(\cot x+3)^2}=\dfrac{x\csc^2x+\cot x+3}{(\cot x+3)^2}$