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how to do partial derivative. For a function of many variables. Using the rules for ordinary differentiation we know that.
The first line in red says. D f x n gives the multiple derivative. F x x y 2 y 3 x.
For the partial derivative at 1 1 that leaves y constant the corresponding tangent line is parallel to the xz -plane.
D g d x x 2 b 3 x. Now we remember that b y and substitute y back in to conclude that. F y x 0 y 0 lim h 0 f x 0 y 0 h f x 0 y 0 h. D f x n gives the multiple derivative.