chapter3(3) - x ) and the number of genera ( y ) comprising...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH1010: Chapter 3 cont… 1 DIFFERENTIATION RULES cont … Implicit Differentiation (Section 3.6 of Stewart, pg.227) So far, we’ve always been given ) ( x f y = explicitly, but what if y is defined implicitly as a function of x ? Example: 1 2 2 = + y x . Find y . A new idea: Use implicit differentiation! STEPS: 1. Differentiate both sides with respect to x . (Keep in mind that y is a function of x .) 2. Solve for y .
Background image of page 1

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

View Full DocumentRight Arrow Icon
MATH1010: Chapter 3 cont… 2 Example: Find the slope of the tangent line at ( 2 , 0 = = y x ) for the curve defined by: x x x y y y 2 3 2 2 2 3 2 3 + = + Example: If ) ( sin 3 2 y e y y x = , find y .
Background image of page 2
MATH1010: Chapter 3 cont… 3 Application: The relationship between the number of species in a genus (
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ) and the number of genera ( y ) comprising x species is given by k y x a = where a and k are constants. Find dx dy . [Source: Calculus for the Life Sciences, by R. Greenwell, N. Ritchey, and M. Lial, 2003] Application: Suppose that van der Waals equation for a specific gas is 7 . 9 ) 03 . ( 5 2 = + V V P Thinking of the volume V as a function of pressure P , use implicit differentiation to find the derivative dP dV at the point ) 1 , 5 ( [Source: Calculus: Concepts & Connections by R. Smith and R. Minton, 2006]...
View Full Document

This note was uploaded on 09/13/2008 for the course MATH 1010u taught by Professor Kim during the Spring '08 term at Trinity University.

Page1 / 3

chapter3(3) - x ) and the number of genera ( y ) comprising...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online