find derivative of!!!!!!!!!!!!!!!!!!

Question

4cos(2x)sin(y)=7

Answer 1

4cos(2x) sin(y) = 7

Divide each side by cos(2x)

4cos(2x)sin(y) / cos(2x)  = 7 / cos(2x)

Recall:Trigonometry identity formulas secA  = 1 / cosA

4sin(y) = 7sec(2x)

Diferenciate to each side with respective x

Recall: from derivative formulas d /dx(sin(x) = cos(x) and d / dx (sec(2x)) = 2sec(2x)tan(2x)

4cos(y)(dy / dx) = 7sec(2x)tan(2x) * 2

Divide each side by 2

2cos(y)(dy / dx) = 7 sec(2x) tan(2x)

Divide each side by 2cos(y)

2cos(y)(dy / dx) / 2cos(y) =  [7sec(2x) tan(2x)] / 2cos(y)

dy / dx = 7/2 sec(2x) tan(2x) / cos(y)

The derivative is dy / dx = 7/2 sec(2x) tan(2x) / cos(y).