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By: Jennifer Larson. Fun With derivatives. START !. I’ve used this program before. I’m a first time user. WELCOME!.

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Presentation Transcript
slide2

I’ve used this program before

I’m a first time user

slide3

WELCOME!

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!

Home

Next

Back

what do you want to learn
What do you want to learn?

Pre-derivative review

Definition of a derivative

Derivative of a constant

Power rule

Sum rule

Difference rule

quiz

slide5

Review

Start!

slide6

Remember…

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

xmxn=xm+n

xm = xm-n

xn

(xm)n = xmn

x-n = 1

xn

common derivative notations
Common Derivative Notations

dy d (f(x)) f’(x)

dxdx

Dxy y’

In this lesson, we will use y’.

y ax n y nax n 1

Power

y=axny’=naxn-1

Function

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

try it out
Try it out!

If y=x2, find y’.

x32x2x23x3

great job
Great Job!

Move On

slide18
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!
great job1
Great Job!

Move On

oops remember
Oops! Remember…

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

y’= f’(x)+g(x)

Take derivative of each individually and

add them together!!

Try Again!

great job2
Great Job!

Move On

sum rule
Sum Rule

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!

slide28
Summary…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
Quiz Directions
  • 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
great job3
Great Job!

Next Question

great job4
Great Job!

Next Question

great job5
Great Job!

Next Question

take the power times the function to one less power y 10x 32
Take the power times the function to one less power…y= 10x3

Power

Try Again!

Remember… The derivative of every constant is zero!!

Function

great job6
Great Job!

Next Question

take the power times the function to one less power y 10x 33
Take the power times the function to one less power…y= 10x3

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

Power

Try Again!

Function

great job7
Great Job!

Next Question

take the power times the function to one less power y 10x 34
Take the power times the function to one less power…y= 10x3

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

Power

Try Again!

Function

great job8
Great Job!

Next Question

take the power times the function to one less power y 10x 35
Take the power times the function to one less power…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

great job9
Great Job!

Next Question

take the power times the function to one less power y 10x 36
Take the power times the function to one less power…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

great job10
Great Job!

Next Question

oops remember the derivative of every constant or any number is zero
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
9. Find the derivative of the line (remember the most common form of a derivative we know…)

2

1

1

2

X213x20

great job11
Great Job!

End Quiz

slide57

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
References:
  • 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
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