Category:Chain Rule for Partial Derivatives

This category contains pages concerning Chain Rule for Partial Derivatives:

Let $F: \R^2 \to \R$ be a real-valued function of $2$ variables.

Let $X: \R^2 \to \R$ and $Y: \R^2 \to \R$ also be real-valued functions of $2$ variables.

Let $F = \map f {x, y}$ be such that:

$\ds x$

$=$

$\ds \map X {u, v}$

$\ds y$

$=$

$\ds \map Y {u, v}$

Then:

$F = \map F {u, v}$

and:

$\ds \dfrac {\partial F} {\partial u}$

$=$

$\ds \dfrac {\partial f} {\partial x} \dfrac {\partial X} {\partial u} + \dfrac {\partial f} {\partial y} \dfrac {\partial Y} {\partial u}$

$\ds \dfrac {\partial F} {\partial v}$

$=$

$\ds \dfrac {\partial f} {\partial x} \dfrac {\partial X} {\partial v} + \dfrac {\partial f} {\partial y} \dfrac {\partial Y} {\partial v}$

Pages in category "Chain Rule for Partial Derivatives"

The following 3 pages are in this category, out of 3 total.