Derivative of multivariable function

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# Derivative of multivariable function

Submitted by neilamezghni on Tue, 06/08/2010 - 18:50

Forums:

Hello,

I have a function f(t,x1(t),x2(t),x3(t)), what it is the derivtive of f with respect to time t?

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## Versions

(v1) by neilamezghni 2010-06-08

## Re: Derivative of multivariable function

Correction to the left side:

By the chain rule (http://planetmath.org/encyclopedia/ChainRuleSeveralVariables.html), you have

df/dt = f'_t+f'_{x_1}df_1/dt+f'_{x_2}dx_2/dt+f'_{x_3}dx_3/dt.

Jussi

## Re: Derivative of multivariable function

By the chain rule (http://planetmath.org/encyclopedia/ChainRuleSeveralVariables.html), you have

df/dx = f'_t+f'_{x_1}df_1/dt+f'_{x_2}dx_2/dt+f'_{x_3}dx_3/dt.

Jussi