Lecture 14 How does f vary if we change x y or z f x y z on set of x y z where g x y z constant Change x and keep y and g constant therefore we will have to also vary z Example f x y x z and g xyz 6 Find f x First method use g 6 to solve for z in general it will be too complicated to just solve for z in terms of x and y Second method use differentials Now nd f y General formula f f x f y f z and 0 g g x g y g z Third method use the chain rule We know that z is somehow dependent on x and y we do not need a whole formula for z we simply need z x Example A triangle with variables a b c and 0 which are related by the law of cosines a b 2abcos0 c same formula as highlighted above dg 2a 2bcos0 a 2b 2acost0 db 2c c 2absin0 0 0 Find f a we know that b c g 0 f a
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