implicit differentiation

Quick Reference

When x and y satisfy a single equation, it may be possible to regard this as defining y as a function of x with a suitable domain, even though there is no explicit formula for y. In such a case, it may be possible to obtain the derivative of y by a method, called implicit differentiation, that consists of differentiating the equation as it stands and making use of the chain rule. For example, if xy2+x2y3−1=0, thenand so, if 2xy+3x2y2 ≠ 0,

Subjects: Mathematics.

Reference entries