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Chain Rule with Dependent Variables

CHAIN RULE WITH DEPENDENT VARIABLES

Let

x = f(t), y = g(t) = G(x).

Assume g'(t) and G'(x) exist. Then

02_differentiation-345.gif

where dx/dt, dy/dt are computed with t as the independent variable, and dy/dx is computed with x as the independent variable.

Let us work Examples 1 and 2 again with dependent variables.
Home Differentiation Chain Rule Chain Rule with Dependent Variables

Last Update: 2006-11-05