This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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)....
View
Full
Document
This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.
 Fall '09
 forgot
 Math, Calculus, Linear Algebra, Algebra

Click to edit the document details