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21-05-2018
Mathematics

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

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LammettHash LammettHash

24-05-2018

I'm assuming

[tex]f(x)=\dfrac x{\cot x+3}[/tex]

By the quotient rule, the derivative [tex]f'(x)[/tex] is

[tex]\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}[/tex]

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