MATH 20C Lecture 15

${\lim }_{(x,y)\to (0,0)}{x}^2{y}^2\ln (x^2+y^2)$

Note




Since

Since ,

by the squeeze theorem

14.3 Partial Derivatives

Partial Derivative

is called the partial derivative of with respect to (w.r.t.) .
is called the partial derivative of with respect to (w.r.t.) .

Partial Derivative Notation

Notation

Note that

By definition, to compute , we treat as a constant, and take the derivative w.r.t. . Similarly, to compute , we differentiate w.r.t. , assuming is a constant.

Higher Order Partial Derivatives

,

Mixed Partials

,

Lebniz Notation

Higher Derivatives