Implicit Differentiation

Implicit differentiation is very useful when you want to find the derivative dy/dx, but x and y are not related in a simple manner, like y = ƒ(x). Rather, x and y might be related by some more complicated expression, like sin(x + y) = x, in which it might be tricky to write y in terms of x. This is the ideal time to use implicit differentiation because it allows us to go straight to differentiating both sides rather than worrying about isolating y, which could be difficult.