6. Derivatives of Products and Quotients
by M. Bourne
PRODUCT RULE
If u and v are two functions of x, then the derivative of the product uv is given by...
Don't miss...
Later in this section:
Quotient Rule
In words, this can be remembered as:
"The derivative of a product of two functions is the first times the derivative of the second, plus the second times the derivative of the first."
Example 1:
If we have a product like
y = (2x2 + 6x)(2x3 + 5x2)
we can find the derivative without multiplying out the expression on the right.
LiveMath does things in a slightly different order...
Example 2:
Find the derivative of 
NOTE:
We can write the product rule in many different ways:
OR
… etc.
QUOTIENT RULE
(A quotient is just a fraction.)
If u and v are two functions of x, then the derivative of the quotient u/v is given by...
In words, this can be remembered as:
"The derivative of a quotient equals bottom times derivative of top minus top times derivative of the bottom, divided by bottom squared."
Example 1:
We wish to find the derivative of the expression:
Play with this example on the Differentiation Java applet page.
Example 2:
Find 
if 
.
Play with this example on the Differentiation Java applet page.
Let's also see this in LiveMath.
NOTE:
You will also see the quotient rule written as:
OR
etc.
Book mark this page in Del.icio.us, Furl, Digg, StumbleUpon, whatever...
Didn't find what you are looking for? Try search:
Need a break? Play a math game. Well, they all involve math... No, really!
Home |
Sitemap |
About & Contact |
Feedback & questions |
Privacy
Users online:
19. Highest ever: 68, on 20 May 2008
Page last modified: 16 November 2007
Valid HTML 4.01
| Valid CSS