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# Fun With derivatives - PowerPoint PPT Presentation

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### Fun With derivatives

START!

I’m a first time user

This program was designed to give students like you a fun way to learn calculus! Navigate through the program by clicking the icons at the bottom, left-hand corner of the screen!

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Next

Back

Pre-derivative review

Definition of a derivative

Derivative of a constant

Power rule

Sum rule

Difference rule

quiz

Start!

Slope=m= y2-y1 = y x2-x1 = x

xmxn=xm+n

xm = xm-n

xn

(xm)n = xmn

x-n = 1

xn

Find Out!

Derivative slope!!- how much a quantity is changing at some given point

Common Notations

Common Derivative Notations slope!!

dy d (f(x)) f’(x)

dxdx

Dxy y’

In this lesson, we will use y’.

POWER RULE!!! slope!!x2, 2x3

GO!

Power slope!!

y=axny’=naxn-1

Function

*Take the power, times the function to one less power*

Try it out! slope!!

If y=x2, find y’.

x32x2x23x3

Great Job! slope!!

Move On

Oops! Remember…. slope!!y=axny’=n·a·xn-1

Try Again

Sum Rule! slope!!y=x2+3x y=3x3+4

GO!

y= (f(x)+g(x)) slope!!y’= f’(x)+g(x)Find the derivative of each part, just like from the power rule, and add them together!

Try it out! slope!!If y=3x2+2x, find y’.6x+2x3+2x269x3+4x2

Great Job! slope!!

Move On

Oops! Remember… slope!!

y= (f(x)+g(x))

y’= f’(x)+g(x)

Take derivative of each individually and

add them together!!

Try Again!

Difference Rule! slope!!y=3x3-2 y=14x4-12x2

GO!

y= f(x)-g(x) slope!!y’= f’(x)-g’(x)Find the derivative of each part and subtract respectively!

Try it out! slope!!If y=12x2-24x, find y’.13x324x4824x-24

Great Job! slope!!

Move On

Oops! Remember… slope!!It’s just like the but we subtract instead of add!

Sum Rule

Sum Rule slope!!

y= (f(x)+g(x))y’= f’(x)+g(x)Find the derivative of each part, just like from the power rule, and add them together!

Summary… slope!!Power Rule Sum Rule Difference Ruley=axny= (f(x)+g(x)) y= f(x)-g(x)y’=naxn-1 y’= f’(x)+g(x) y’= f’(x)-g’(x)

Quiz Directions slope!!

• You may use separate pencil and paper if needed

• Click the answer you believe is correct

• Keep track of how many you get correct the first try

1. y=10x slope!!3y’=20x210x30x260

Great Job! slope!!

Next Question

Take the power times the function to one less power… slope!!y= 10x3

Power

Try Again!

Function

2. y=13x slope!!7y’=91x613x8x713/8 x8

Great Job! slope!!

Next Question

Take the power times the function to one less power… slope!!y= 10x3

Power

Try Again!

Function

3. y=35x slope!!2+12y’=35x270x70x+1212

Great Job! slope!!

Next Question

Take the power times the function to one less power… slope!!y= 10x3

Power

Try Again!

Remember… The derivative of every constant is zero!!

Function

4. y=10x slope!!2+13xy’=20x2+1320x+1310x2+13x

Great Job! slope!!

Next Question

Take the power times the function to one less power… slope!!y= 10x3

The Sum Rule says to take the derivative of each part and add them together!

Power

Try Again!

Function

5. y=6x slope!!4+13x+20y’=24x3+1324x3+13x+2024x3+13x

Great Job! slope!!

Next Question

Take the power times the function to one less power… slope!!y= 10x3

The Sum Rule says to take the derivative of each part and add them together!

Power

Try Again!

Function

6. y=13x slope!!2-14xy’=13x+1426x-1413x3-14x2

Great Job! slope!!

Next Question

Take the power times the function to one less power… slope!!y= 10x3

The Difference Rule says to take the derivative of each part and take subtract, instead of adding like the Sum Rule

Power

Try Again!

Function

7. y=20x slope!!6-15x3-100y’=120x5-45x2120x5-45x2-10020x-15

Great Job! slope!!

Next Question

Take the power times the function to one less power… slope!!y= 10x3

The Difference Rule says to take the derivative of each part and take subtract, instead of adding like the Sum Rule

Power

Try Again!

Function

8. y=1,000,000-x slope!!y’=01,000,000-1x

Great Job! slope!!

Next Question

Oops! Remember… The derivative of every constant, or any number, is zero.

Power is 1

Take the power times the function to one less power…

-x

Function to one less power is x0, or 1

9. Find the derivative of the line (remember the most common form of a derivative we know…)

2

1

1

2

X213x20

Great Job! common form of a derivative we know…)

End Quiz

Oops! common form of a derivative we know…)Remember, y’ is the same as slope! ( y)

x

You’re done with the quiz! If you correctly answered 7 or more on the first try, click here to end this lesson. If you answered less than 7 correctly on the first try, click here to review!

References: more on the first try, click

• http://www.karlscalculus.org/calc4_4.html

• http://www.sites4teachers.com/links/redirect.php?url=http://www.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calculus.html

• http://images.google.com/images?q=derivative&gbv=2&ndsp=18&hl=en&start=180&sa=N