How do you differentiate #f(x)=(x+cosx)/(x^2+3)# using the quotient rule?

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Answer 1 · 2016-11-10T03:56:28

#((1-sinx))/(x^2+3) - ((x+cosx)2x)/(x^2+3)^2#

Quotient rule states:
#f/g = (g f' - f g')/g^2#

the derivative of #f(x)=x+cosx# is:
#f'(x)=1-sinx#

the derivative of #g(x)=x^2+3# is:
#g'(x)=2x#

Now plug in:

#((x^2+3)(1-sinx) - (x+cosx)2x)/(x^2+3)^2#

#((x^2+3)(1-sinx))/(x^2+3)^2 - ((x+cosx)2x)/(x^2+3)^2#

#((1-sinx))/(x^2+3) - ((x+cosx)2x)/(x^2+3)^2#