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

1 Answer
Nov 10, 2016

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

Explanation:

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