# Calculus/Multivariable Calculus/Chain Rule

### Rules of taking JacobiansEdit

If * f* :

**R**

^{m}→

**R**

^{n}, and

*h*(

*x*) :

**R**

^{m}→

**R**are differentiable at '

**p'**:

Important: make sure the order is right - matrix multiplication is not commutative!

#### Chain ruleEdit

The chain rule for functions of several variables is as follows. For * f* :

**R**

^{m}→

**R**

^{n}and

*:*

**g****R**

^{n}→

**R**

^{p}, and

*o*

**g***differentiable at*

**f***, then the Jacobian is given by*

**p**Again, we have matrix multiplication, so one must preserve this exact order. Compositions in one order may be defined, but not necessarily in the other way.