Arithmetic Question for Finding Derivative using Quotient Rule

[Joe_K]

Homework Statement

Find dy/dx for the following function:

y = (11-cos(x))/(2+cos(x))

Homework Equations

Quotient Rule:

y'= ((g(x))(f'(x)) - (f(x))(g'(x)))/ (g(x)^2)

The Attempt at a Solution

I used the quotient rule to come up with this:

y'= ((2+cos(x))(sin(x)) - (11-cos(x))(-sin(x))) / ((2+cos(x))^2)


Now, the trouble that I am having is simplifying this.

The final answer should turn out to be :

(13sin(x))/(cos(x)+2)^2

I am overlooking some basic arithmetic here, but I can't seem to find out what I am missing. Am I supposed to multiply out the expressions first and then combine like terms? Basically, how do I go from the expanded version to the simplified version? Thank you

 

[danago]

Yes try expanding it; simplifying it to the required expression is just a matter of collecting like terms

 

[SammyS]

Your denominator looks to be in the same form as the desired answer.

Play around with the numerator.