implicit-diff-notes - OPMT 5701 Lecture Notes Implicit...

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OPMT 5701 Lecture Notes Implicit Di f erentiation This section assumes the students have read the section on implicit di f erentiation in Chap- ter 13 of the text book. Suppose we have the following: 2 y +3 x =12 we can rewrite it as 2 y =1 2 3 x y =6 3 2 x Now we have y = f ( x ) and we can take the derivative dy dx = 3 2 Lets consider an alternative. We know that y is a function of x or, y = y ( x ) and the derivative of y is dy dx . If we return to our original equation, 2 y x ,wecand i f erentiate it IMPLICITLY in the following manner 2 dy dx dx dx = d (12) dx =0 2 dy dx +3 = 0 μ dx dx rearrange to get dy dx by itself 2 dy dx = 3 dy dx = 3 2 which is what we got before! Here is a few more examples: 1. y 2 + x 2 =3 6 2 y dy dx +2 x dx dx μ remember d (36) dx 2 y dy dx x dy dx = 2 x 2 y = x y 2. 5 y 3 +4 x 5 = 250 15 y 2 dy dx +20 x 4 dy dx = 20 x 4 15 y 2 = 4 x 4 3 y 2 1
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3. y 1 / 2 2 x 2 +5 y =1 5 1 2 y 1 / 2 dy dx 4 x dy dx =0 μ 1 2 y 1 / 2 dy dx 4 x dy dx = 4 x ¡ 1 2 y 1 / 2 ¢
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This note was uploaded on 03/03/2012 for the course ECON 345 taught by Professor Wendywu during the Fall '11 term at Wilfred Laurier University .

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implicit-diff-notes - OPMT 5701 Lecture Notes Implicit...

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