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

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

User Vannesa
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1 Answer

3 votes
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)
User Michael Landis
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