06Implicit Differentiation

# 06Implicit Differentiation - y ′′ Ex Find y ′′ if 4...

This preview shows pages 1–2. Sign up to view the full content.

I MPLICIT D IFFERENTIATION Some functions are expressed explicitly in terms of another variable (y = ), but others are defined implicitly by a relation between x and y such as . 25 2 2 = + y x We could solve for y and then take the derivative, or we could use a process called implicit differentiation . Differentiate both sides of the equation with respect to x , then solve the resulting equation for y . Ex . . 25 2 2 = + y x 2 25 x y - ± = Ex . If 3 3 5 x y + = , use implicit differentiation to find

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y ′′ . Ex . Find y ′′ if 4 4 16 x y + = . Ex . a) Find dx dy if 36 2 5 4 5 = + + y y x x b) Find the slope of the tangent to the curve 36 2 5 4 5 = + + y y x x at the point (1, 2). Ex . Find the slope of the tangent line to 1 3 2 2 2 3 = + + +-x y x xy y at the point (1, 2). Assign: p.217 # 9, 11-16, 21, 23; Worksheets – implicit differentiation...
View Full Document

## This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

### Page1 / 2

06Implicit Differentiation - y ′′ Ex Find y ′′ if 4...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online