Implicit Differentiation

Question

Find dy/dx by implicit differentiation

tan(x - y) = y / 1 + x²

dy/dx = ?

Answer 1

tan(x - y) = y/(1 + x²);

sec²(x - y)(1 - y') = [y'(1 + x²) - 2xy]/(1 + x²)²;

sec²(x - y) + 2xy/(1 + x²)² = y'[sec²(x - y) + 1/(1 + x²)].

From here y' = ...

Answer 2

tan(x-y) = y/(1+x^2)

[tan(x-y)]'=0 = (1+x^2)y'+ y(2x)

y' = dy/dx = -2xy/(1+x^2)