Please see the attached file.
Given a function from R^n to R^m, the derivative is no longer simply a function as it is in introductory calculus. Instead, the derivative at a point is a linear map, which can be represented by a matrix of partial derivatives. There is a higher dimensional analogue of the 1 dimensional Chain rule which can be used to calculate the derivative map of a composite function. The solution comprises a one page Word document with equations written in Mathtype illustrating the use of the higher dimensional Chain rule.