Differentiate this trig problem !! Help?

Question

17 cos (x) sin (y) =12 I am clueless I just missed this on a test and had no clue how to do it!!

Answer 1

We need to use implicit differentiation here.

17 cos x sin y = 12
Differentiate w.r.t. x to get
17 (-sin x) sin y + 17 cos x (cos y dy/dx) = 0
=> cos x cos y dy/dx = sin x sin y
=> dy/dx = (sin x sin y) / (cos x cos y) = tan x tan y.