Find dy/dx when

Question

tan(x + y) = 3x − 2y .?  

Answer 1

The equation is tan(x + y) = 3x - 2y.

Differentiate with respect to x.

sec²(x + y)*(1+y') = 3 - 2y'

sec²(x + y) + y' * sec²(x + y) = 3 - 2y'

y' * sec²(x + y) + 2y' = 3 - sec²(x + y)

y' * [sec²(x + y) + 2] = 3 - sec²(x + y)

y' = [3 - sec²(x + y)] / [sec²(x + y) + 2].