Calculus/Multivariable Calculus/Chain Rule
Rules of taking Jacobians[edit | edit source]
If f : Rm → Rn, and h(x) : Rm → R are differentiable at 'p':
Important: make sure the order is right - matrix multiplication is not commutative!
Chain rule[edit | edit source]
The chain rule for functions of several variables is as follows. For f : Rm → Rn and g : Rn → Rp, 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.