Calculus/Multivariable Calculus/Chain Rule

Rules of taking Jacobians 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 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.