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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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By jennifer larson

By: Jennifer Larson

Fun With derivatives

START!


I’ve used this program before

I’m a first time user


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


Review

Start!


Remember…

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

xmxn=xm+n

xm = xm-n

xn

(xm)n = xmn

x-n = 1

xn




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

Common Notations


Common derivative notations
Common Derivative Notations slope!!

dy d (f(x)) f’(x)

dxdx

Dxy y’

In this lesson, we will use y’.



Power rule x 2 2x 3
POWER RULE!!! slope!!x2, 2x3

GO!


Y ax n y nax n 1

Power slope!!

y=axny’=naxn-1

Function

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


Try it out
Try it out! slope!!

If y=x2, find y’.

x32x2x23x3


Great job
Great Job! slope!!

Move On


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

Try Again


Sum rule y x 2 3x y 3x 3 4
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 if y 3x 2 2x find y 6x 2 x 3 2x 2 6 9x 3 4x 2
Try it out! slope!!If y=3x2+2x, find y’.6x+2x3+2x269x3+4x2


Great job1
Great Job! slope!!

Move On


Oops remember
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 y 3x 3 2 y 14x 4 12x 2
Difference Rule! slope!!y=3x3-2 y=14x4-12x2

GO!


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


Try it out if y 12x 2 24x find y 13x 3 24x 48 24x 24
Try it out! slope!!If y=12x2-24x, find y’.13x324x4824x-24


Great job2
Great Job! slope!!

Move On


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

Sum Rule


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
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 3 y 20x 2 10x 30x 2 60
1. y=10x slope!!3y’=20x210x30x260


Great job3
Great Job! slope!!

Next Question


Take the power times the function to one less power y 10x 3
Take the power times the function to one less power… slope!!y= 10x3

Power

Try Again!

Function


2 y 13x 7 y 91x 6 13x 8 x 7 13 8 x 8
2. y=13x slope!!7y’=91x613x8x713/8 x8


Great job4
Great Job! slope!!

Next Question


Take the power times the function to one less power y 10x 31
Take the power times the function to one less power… slope!!y= 10x3

Power

Try Again!

Function


3 y 35x 2 12 y 35x 2 70x 70x 12 12
3. y=35x slope!!2+12y’=35x270x70x+1212


Great job5
Great Job! slope!!

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… slope!!y= 10x3

Power

Try Again!

Remember… The derivative of every constant is zero!!

Function


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


Great job6
Great Job! slope!!

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… 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 4 13x 20 y 24x 3 13 24x 3 13x 20 24x 3 13x
5. y=6x slope!!4+13x+20y’=24x3+1324x3+13x+2024x3+13x


Great job7
Great Job! slope!!

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… 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 2 14x y 13x 14 26x 14 13x 3 14x 2
6. y=13x slope!!2-14xy’=13x+1426x-1413x3-14x2


Great job8
Great Job! slope!!

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… 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 6 15x 3 100 y 120x 5 45x 2 120x 5 45x 2 100 20x 15
7. y=20x slope!!6-15x3-100y’=120x5-45x2120x5-45x2-10020x-15


Great job9
Great Job! slope!!

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… 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 y 0 1 000 000 1 x
8. y=1,000,000-x slope!!y’=01,000,000-1x


Great job10
Great Job! slope!!

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! common form of a derivative we know…)

End Quiz


Oops remember y is the same as slope y
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
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


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