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{|
 
{|
 
|-
 
|-
−
! colspan="2" style="background-color: rgb(228, 188, 126); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" | Laplace Transform Pairs and Properties
+
! style="background-color: rgb(228, 188, 126); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Laplace Transform Pairs and Properties
 
|-
 
|-
−
! colspan="2" style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" | General Rules
+
! style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | General Rules
 
|-
 
|-
 
| Derivative of a constant  
 
| Derivative of a constant  
Line 16: Line 16:
 
| <math>\frac{d}{dx}\left( c_1 u_1+c_2 u_2 \right)  = c_1 \frac{d}{dx}\left( u_1 \right)+c_2 \frac{d}{dx}\left( u_2 \right), \ \text{ for any constants }c_1, c_2</math>
 
| <math>\frac{d}{dx}\left( c_1 u_1+c_2 u_2 \right)  = c_1 \frac{d}{dx}\left( u_1 \right)+c_2 \frac{d}{dx}\left( u_2 \right), \ \text{ for any constants }c_1, c_2</math>
 
|-
 
|-
−
| please continue  
+
| Please continue
−
| put new rule here
+
| write a rule here
 +
|}
 +
{|
 
|-
 
|-
−
! colspan="3" style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" |Derivatives of trigonometric functions
+
! style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="3" | Derivatives of trigonometric functions
 
|-
 
|-
 
| sine  
 
| sine  
−
| <span class="texhtml">sin''u''</span>  
+
| <span class="texhtml">sin'' u''</span>  
 
| align="left" | <math>\cos u \frac{du}{dx}</math>
 
| align="left" | <math>\cos u \frac{du}{dx}</math>
 
|-
 
|-
−
| please continue
+
|
−
| write a function here  
+
| add function here  
−
| write its derivative here
+
| derivative here
−
|}
+
−
 
+
−
<br>
+
−
 
+
−
{| cellspacing="1" cellpadding="1" border="0"
+
−
|+ Derivative of trigonometric functions
+
 
|-
 
|-
−
! scope="col" | Name
+
! style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="3" | Derivatives of exponential and logarithm functions
−
! scope="col" | Function
+
−
! scope="col" | Derivative
+
 
|-
 
|-
−
| sine
+
| exponential
−
| <span class="texhtml">sin''u''</span>  
+
| <span class="texhtml">''e''<sup>''u''</sup></span>  
−
| <math>\cos u \frac{du}{dx}</math>
+
| <math>e^u \frac{du}{dx}</math>
 
|-
 
|-
−
| please continue
+
|
−
| write a function here  
+
| add function here  
−
| write its derivative here
+
| derivative here
−
|}
+
−
 
+
−
{| cellspacing="1" cellpadding="1" border="0"
+
−
|+ Derivative of exponentiel and logarithm functions
+
 
|-
 
|-
−
! scope="col" | Name
+
! style="background-color: rgb(238, 238, 238); background-image: none; background-repeat: repeat; background-attachment: scroll; background-position: 0% 0%; -moz-background-size: auto auto; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="3" | Derivatives of hyperbolic functions
−
! scope="col" | Function
+
−
! scope="col" | Derivative
+
 
|-
 
|-
 
| exponential  
 
| exponential  
Line 59: Line 47:
 
| <math>e^u \frac{du}{dx}</math>
 
| <math>e^u \frac{du}{dx}</math>
 
|-
 
|-
−
| please continue
+
|
−
| write a function here  
+
| add function here  
−
| write its derivative here
+
| derivative here
 
|}
 
|}

Revision as of 07:11, 26 October 2010

Table of Derivatives

Laplace Transform Pairs and Properties
General Rules
Derivative of a constant $ \frac{d}{dx}\left( c \right) = 0, \ \text{ for any constant }c $
$ \frac{d}{dx}\left( c x \right) = c, \ \text{ for any constant }c $
Linearity $ \frac{d}{dx}\left( c_1 u_1+c_2 u_2 \right) = c_1 \frac{d}{dx}\left( u_1 \right)+c_2 \frac{d}{dx}\left( u_2 \right), \ \text{ for any constants }c_1, c_2 $
Please continue write a rule here
Derivatives of trigonometric functions
sine sin u $ \cos u \frac{du}{dx} $
add function here derivative here
Derivatives of exponential and logarithm functions
exponential eu $ e^u \frac{du}{dx} $
add function here derivative here
Derivatives of hyperbolic functions
exponential eu $ e^u \frac{du}{dx} $
add function here derivative here
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Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett