Calculus/Multivariable Calculus/Chain Rule

Rules of taking JacobiansEdit

If f : RmRn, and h(x) : RmR are differentiable at 'p':

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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 : RmRn and g : RnRp, and g o f differentiable at p, then the Jacobian is given by

 

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.