lecture16 - Lecture 16: The Chain Rule Chapter 3, Section...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 16: The Chain Rule Chapter 3, Section 16 Consider the composite function h ( x ) = p x 2 + 2 x ¡ 3. How to difierentiate? To get an idea, flnd H 0 ( x ) if H ( x ) = ( x 2 + 2 x ¡ 3) 2 .
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Theorem (The Chain Rule) : If g is difierentiable at x and f is difierentiable at g ( x ), then the composite function F = f g = f ( g ( x )) is difierentiable and F 0 ( x ) = There is a second version of the Chain Rule. To illustrate, think of a disaster such as an oil leak from a well, where environmental damage occurs over time. Let y be the cost of the cleanup of the oil in dollars. y is a function of the number of gallons spilled, u . But u is a function of the number of days the well has been leaking, x . We can think of y is a function of x , so can we flnd the rate at which y is changing with respect to x ?
Background image of page 2
3 Chain Rule (rate of change version) If y = f ( u ) and u = g ( x ) are difierentiable functions, then ex. Find h 0 ( x ) for h ( x ) = p x 2 + 2 x ¡ 3. ex. If f ( x ) = (2 e x ¡ 3 x ) 5 , flnd f 0 (0).
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 These are examples of the following: Power Rule combined with the Chain Rule If n
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 13

lecture16 - Lecture 16: The Chain Rule Chapter 3, Section...

This preview shows document pages 1 - 5. Sign up to view the full document.

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