For 10 points, name the rule for differentiation of the composition of two functions which states that, for functions f [eff] and g [gee], the derivative of the quantity f composed with g is equal to the derivative of f of g of x times the derivative of g of x.
The generalized variety of this allows one to state the Jacobian matrix of functions y [why] with respect to variables x [ecks] as the product of the Jacobian matrix of y with respect to u [you] and the Jacobian matrix of u with respect to x. For one variable, this can be derived most directly using the mean value theorem, and its inverse is the integral u substitution. For 10 points, name the rule for differentiation of the composition of two functions which states that, for functions f [eff] and g [gee], the derivative of the quantity f composed with g is equal to the derivative of f of g of x times the derivative of g of x.
The generalized variety of this allows one to state the Jacobian matrix of functions y [why] with respect to variables x [ecks] as the product of the Jacobian matrix of y with respect to u [you] and the Jacobian matrix of u with respect to x.
{chain rule}