← Calculo
Implicit Differentiation

Slopes Without y = f(x)

A circle isn’t a function — two y’s for each x. Yet every point still has a tangent. Differentiate the relation F(x,y)=0 and the slope falls out: dy/dx = −Fₓ/Fₔ.

slide the point · the tangent’s slope is −Fₓ/Fₔ
F(x,y)=0 tangent point