Expert: Paul Klarreich - 9/6/2007

Question
could you please give me the derivatives formulas and a example of how to use the quotient rule
thanks

Answer
Questioner:   Elmer
Category:  Calculus
Private:  No
 
Subject:  derivatives
Question:  could you please give me the derivatives formulas and a example of how to use the quotient rule
thanks
.......................
Hi, Elmer,

For the complete set of derivative formulas, you will just have to look in your textbook.  As to the quotient rule, which you should learn to love, my recommendation is this:

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1. Start by writing this pattern with empty parentheses:
dy   ()() - ()()
-- = -------------
dx       ()^2

2. Then fill in the components:

dy   (bottom)(derivatve of top) - (top)(derivative of bottom)
-- = --------------------------------------------------------
dx                     (bottom)^2

with the proper expressions.

3. Then do the proper simplifications.

Here is one example:  Use the quotient rule to obtain the formula:

D(tan x) = sec^2(x)
               sin x
Let y = tan x = ------
               cos x

Differentiate:

1. Start by writing this pattern with empty parentheses:
dy   ()() - ()()
-- = -------------
dx       ()^2

2. Then fill in the components:

dy   (cos x)(cos x) - (sin x)(- sin x)
-- = ---------------------------------
dx           (cos x)^2

3. Simplify: (I assume you have done your homework and know your trig.)

dy   cos^2(x) + sin^2(x)
-- = --------------------
dx       cos^2(x)

dy       1
-- = ---------- = sec^2(x)
dx    cos^2(x)