lecture22hout

lecture22hout - MATH 006 Calculus and Linear Algebra...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 22) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 11 Outline 1 Implicit Differentiation Albert Ku (HKUST) MATH 006 2 / 11 Implicit Differentiation Implicit Functions Suppose y = f ( x ). Then dy dx = f ( x ). However, sometimes x and y are related by an equation F ( x , y ) = 0 and we are unable to rewrite it as y = f ( x ). In this case, y is still regarded as a function of x , defined implicitly by the equation. Therefore, we can find dy dx from the given equation. Consider the graph of F ( x , y ) = 0 i.e. a collection of all points such that their coordinates satisfy the given equation. dy dx at ( x , y ) is the slope of the line tangent to the graph at ( x , y ). Albert Ku (HKUST) MATH 006 3 / 11 Implicit Differentiation Implicit Differentiation How can we find dy dx from the given equation? Consider the following example: Example Find the equation of line tangent to the circle x 2 + y 2 = 25 at (3 , 4)....
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This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture22hout - MATH 006 Calculus and Linear Algebra...

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