Tphan046: /* Notes */

2020-07-19T14:51:39Z

Notes

Tphan046: /* Notes */

2020-07-19T14:12:43Z

Notes

Tphan046: Created page with "==The Constant Rule== The derivative of a constant function is zero. That is, $\frac{d}{dx}[c]=0$ where $c$ is a constant '''Example''': Find deriv..."

2020-07-18T15:19:22Z

Created page with "==The Constant Rule== The derivative of a constant function is zero. That is, <math>\frac{d}{dx}[c]=0</math> where <math>c</math> is a constant '''Example''': Find deriv..."

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==The Constant Rule==
The derivative of a constant function is zero. That is, <math>\frac{d}{dx}[c]=0</math> where
<math>c</math> is a constant

'''Example''': Find derivative of

'''1)''' <math>f(x)=5</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|<math style="vertical-align: -5px">f'(x)=0</math>
|-
|}

'''2)''' <math>f(x)=\pi</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|<math style="vertical-align: -5px">f'(x)=0</math>
|-
|}

'''3)''' <math>f(x)=e^2</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|<math style="vertical-align: -5px">f'(x)=0</math>
|-
|}

==The Power Rule==
<math>\frac{d}{dx}[x^n]=nx^{n-1} </math> for <math>n</math> is a real number.

'''Example''': Find derivative of

'''1)''' <math>f(x)=x^5</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|<math style="vertical-align: -5px">f'(x)=(5)x^{5-1}=5x^4</math>
|-
|}

'''2)''' <math>f(x)=x^{1000}</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|<math style="vertical-align: -5px">f'(x)=(1000)x^{1000-1}=1000x^{999}</math>
|-
|}

'''3)''' <math>f(x)=\frac{1}{x^3}</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|We rewrite <math>f(x)=\frac{1}{x^3}=x^{-3}</math>, so
|-
|<math style="vertical-align: -5px">f'(x)=(-3)x^{-3-1}=-3x^{-4}=\frac{-3}{x^4}</math>
|-
|}

==The Constant Multiple Rule==
If <math>f</math> is a differentiable function of <math>x</math> and <math>c</math> is a real
number, then <math>\frac {d}{dx} [cf(x)]=cf'(x)</math> for <math>c</math> is a constant.

'''1)''' <math>f(x)=10x^5</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|<math style="vertical-align: -5px">f'(x)=10\frac {d}{dx}(x^5)=10(5x^4)=50x^4</math>
|-
|}

'''2)''' <math>f(x)=3x^{1000}</math>
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|<math style="vertical-align: -5px">f'(x)=3\frac{d}{dx}(x^1000)=3(1000)x^{1000-1}=3000x^{999}</math>
|-
|}

==The Sum and Difference Rules==

The derivative of the sum or difference of two differentiable functions is the sum or difference
of their derivatives.
<math>\frac{d}{dx}[f(x)+g(x)]=f'(x)+g'(x)</math>

<math>\frac{d}{dx}[f(x)-g(x)]=f'(x)-g'(x)</math>

==Notes==
1) <math>\frac{d}{dx}[x]=1</math> since <math>x^0=1</math>

2) We can use the first derivative to find the slope of the tangent line (first derivative is a function which generates the slope)

3) We usually denote <math>\frac{d}{dx}f(x)</math> as <math>f'(x)</math>

'''This page were made by [[Contributors|Tri Phan]]'''

← Older revision		Revision as of 14:51, 19 July 2020
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	3) We usually denote <math>\frac{d}{dx}f(x)</math> as <math>f'(x)</math>		3) We usually denote <math>\frac{d}{dx}f(x)</math> as <math>f'(x)</math>
		+
		+	[[Math_22\| '''Return to Topics Page''']]

	'''This page were made by [[Contributors\|Tri Phan]]'''		'''This page were made by [[Contributors\|Tri Phan]]'''

@@ Line 92: / Line 92: @@
 ) <math>\frac{d}{dx}[x]=1</math> since <math>x^0=1</math>
-) We can use the first derivative to find the slope of the tangent line (first derivative is a function which generates the slope)
+) The derivative of <math>f</math> is a function that gives the slope of the graph of <math>f</math> at a point <math>(x,f(x))</math>.
 ) We usually denote <math>\frac{d}{dx}f(x)</math> as <math>f'(x)</math>
 '''This page were made by [[Contributors|Tri Phan]]'''

Math 22 Differentiation - Revision history

Tphan046: /* Notes */

Tphan046: /* Notes */

Tphan046: Created page with "==The Constant Rule== The derivative of a constant function is zero. That is, \frac{d}{dx}[c]=0 where c is a constant '''Example''': Find deriv..."

Tphan046: Created page with "==The Constant Rule== The derivative of a constant function is zero. That is, $\frac{d}{dx}[c]=0$ where $c$ is a constant '''Example''': Find deriv..."