## Partial differential of composite function

Posted September 22nd, 2007 by Structure

Let

Suppose that g and f are differentiable functions. Then h is differentiable and partial derivative can be founded by . Each differential is a linear application and is represented by the matrix of partial derivatives.For example

Following composition rule for matrix, we have

This sum expresses the product of a line in with a column in

or more explicitly

If g and f are twice differentiable second order partial differential can be express