MIT
18 02 -
Differentials for a function of one variable
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Lecture 11 Differentials for a function of one variable y f x dy f x dx We can divide by dx Gives us an approximation What about dividing by dy Example y sin x x sin y dx cos y dy Differentials for a function of several variables f x y z df f dx f dy f dz f f x f y f z Example Formula for the derivativve of g f in terms of f and g Now with differentials Now we have a f x y z df f dx f dy f dz but x y and z depend on t Example f x y z x t cost y t sint z t 0 Polar coordinates Determined in terms of r and theta r 0 and 0 0 2 What is f of f x y We know that d Example Example Page 905 33 How does volume change with time V H E HE Suppose H 1 and E 2 and that H 1 6 and E 1 4 Whats V then V E dH 2HEdE E H dt 2HE E dt dV dt E H 2HEE
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