(adsbygoogle = window.adsbygoogle || []).push({}); ?? I don't understand this answer

1. The problem statement, all variables and given/known data

The pdf attached is the answer to a question from a Calculus quiz. (the right hand side is a bit cut off, but the formula is repeated further down)

Edit: the "f(x) = ..., and a=0" part is the solution, not part of the the question.

2. Relevant equations

3. The attempt at a solution

ok. I have no idea what she's doing here. when I do the derivative of the f(x) she gives as the answer, I get

1/2 (1+3cosx)^1/2 is

1/4 ((1+3cosx)^-1/2)(-3sinx) = -3sinx / 4 sqrt(1+3cosx)

which is not even close to the original f'(x) she posted...

can anyone show me how she got that answer? thanks.

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# ? I don't understand this answer

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