Answer to Question #204086 in Calculus for moe

Question

Using imlicit differentiation, which one of the following is the derivative of

$cos(x-2y) = sin(2x + y)$

Answer 1

$cos(x−2y)=sin(2x+y)\\ \text{differentiate with respect to x.}\\ \implies -sin(x−2y)(1-2y')=cos(2x+y)(2+y')\\ \implies -sin(x−2y)+2sin(x−2y)y'-2cos(2x+y)- cos(2x+y)y'=0\\ \implies y'=\frac{sin(x−2y)+2cos(2x+y)}{2sin(x−2y)-cos(2x+y)}$