Dervatervs~
*chain rule
*graphing functions without a given function
*reading a chart
Phrases you want to remember (9/22):
A derivative is defined as the slope of the tangent.
It is the slope at a singular point.
The definition of the derivative is what scientists used before they created the shortcuts.
*chain rule
*graphing functions without a given function
*reading a chart
Phrases you want to remember (9/22):
A derivative is defined as the slope of the tangent.
It is the slope at a singular point.
The definition of the derivative is what scientists used before they created the shortcuts.
Notes from Class Friday (9/2)
Includes:
Includes:
- Power Rule
- Chain Rule
- Polynomial Rule
L'Hôpital's Rule (9/22) UNF
L'Hôpital's Rule states that the limit of the function is equal to the limit of the derivative of the function as x approaches a. Thus, finding the derivative of the function is as simple as finding the derivative of the numerator and the derivative of the denominator. Then, plug in the value of a. |
Formula:
Example 1
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Basic Derivative Rules (9/6)
Some of the basic derivative rules we have not talked about in class.
Some of the basic derivative rules we have not talked about in class.
Basic Derivative Values (9/6)
Higher Order Derivatives Notation (9/6)
Dervatervs of Trig Functions (9/6)
Let's Begin~!
Listed below are the four steps to solving Def of Deriv as h->0. 1. Find the original def of deriv a. identify f(x AND it's power b. identify f(x) 2. Find the original f(x) a. replace the [# in place of x] for [x] b. set f(x and its power equal to f(x) c. solve for x 3. Find derivative of f(x) a. drop power to the front b. subtract 1 from the power 4. Plug in value for x into derivative |
Example One
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Definition of Derivative-The Ms. Nobles Way~ (9/22) UNF
Formula:
for the problem given, plug in [x+h] for all x values
*Note: if h is already given, simply plug in variable x
subtract the original function
distribute
simplify
use shortcut to check
*Note: if h is already given, simply plug in variable x
subtract the original function
distribute
simplify
use shortcut to check
Notes Regarding Def or Deriv, DoD at a Point, and Systems of Equations (9/22)
Ln(x) and e's (11/29)
Things to Know:
ln(x)=y
ln1=0
lne=1
lnex=x
Properties of ln(x)
1. Product Rule: lnxy=lnx+lny
2. Quotient Rule: ln x/y=lnx-lny
3. Reciprocal Rule: ln 1/x=-lnx
4. Power Rule ln(x)r=rlnx
The derivative of lnx is 1/x TIMES the derivative of x.
Ex: d/dx of ln(4x)
=1/ln(4x) TIMES 4
=4/ln(4x)
Easy peasy~
ex2: d/dx of ln(cos2x)
=1/ln(cos2x) TIMES (-sin(2x)) TIMES (2)
=-2sin(2x)/ln(cos2x)
Things to Know:
ln(x)=y
ln1=0
lne=1
lnex=x
Properties of ln(x)
1. Product Rule: lnxy=lnx+lny
2. Quotient Rule: ln x/y=lnx-lny
3. Reciprocal Rule: ln 1/x=-lnx
4. Power Rule ln(x)r=rlnx
The derivative of lnx is 1/x TIMES the derivative of x.
Ex: d/dx of ln(4x)
=1/ln(4x) TIMES 4
=4/ln(4x)
Easy peasy~
ex2: d/dx of ln(cos2x)
=1/ln(cos2x) TIMES (-sin(2x)) TIMES (2)
=-2sin(2x)/ln(cos2x)