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

asked Feb 9, 2019 161k views

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I'm assuming

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

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

is

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

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