How do you differentiate #f(x)=cosx/arctanx# using the quotient rule?

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Answer 1 · 2015-12-13T20:48:37

#f'(x)=-sinx/arctanx-cosx/((1+x^2)arctan^2x)#

According to the quotient rule:

#f'(x)=(arctanxd/dx[cosx]-cosxd/dx[arctanx])/arctan^2x#

Find each derivative.

#d/dx[cosx]=-sinx#

#d/dx[arctanx]=1/(1+x^2)#

Plug back in.

#f'(x)=(-sinxarctanx-cosx/(1+x^2))/arctan^2x#

#f'(x)=-sinx/arctanx-cosx/((1+x^2)arctan^2x)#