Implicit Differentiation

A technique used to find the derivative of a function defined implicitly by an equation involving both x and y.

dy/dx = -x^2/y^2.

Use implicit differentiation: dy/dx = -y/x.

dy/dx = 1/(2y cos(y^2)).

dy/dx = -y/(x + 2y).

A rule for finding the derivative of a composite function: if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

A rule for differentiating products of functions: if u and v are functions of x, then d(uv)/dx = u'v + uv'.

A rule for differentiating quotients of functions: if u and v are functions of x, then d(u/v)/dx = (u'v - uv')/v^2.

It allows us to differentiate equations where y cannot be easily isolated.

Differentiate both sides of the equation with respect to x, treating y as a function of x, and solve for dy/dx.