the chain rule for functions of several variables 1 the chain rule for functions of several variables for functions of a single variable we saw that if y is a ...
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...The chain rule for functions of several variables a single variable we saw that if y is differentiable function u and x say f then derivative with respect to given by dy du differential form dx here one generalization two assume v where in turn are substitution can regard as instance let uv substituting gives only suppose continuous partial derivatives ydu ydv udx vdx quick example above have dv therefore ux now independent this same answer would get differentiating directly question what point using when find direct calculating usually use rather than but often algebraically less complicated also will give theoretical applications below graphical representation so far looked at specific which was three or more each those clarify things us represent situation were pictorially figure on top from arrows indicating associated similarly there an arrow pointing along diagram helps write down follows all possible paths multiply path add products obtained step method t w obtain it formula dt ...