Fun With derivatives

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# Fun With derivatives - PowerPoint PPT Presentation

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
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?

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

Common Notations

Common Derivative Notations

dy d (f(x)) f’(x)

dxdx

Dxy y’

In this lesson, we will use y’.

y=500

y’=0

Power

y=axny’=naxn-1

Function

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

Try it out!

If y=x2, find y’.

x32x2x23x3

Great Job!

Move On

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 Job!

Move On

Oops! Remember…

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

y’= f’(x)+g(x)

Take derivative of each individually and

Try Again!

Great Job!

Move On

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!

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
• 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 Job!

Next Question

Power

Try Again!

Function

Great Job!

Next Question

Power

Try Again!

Function

Great Job!

Next Question

Power

Try Again!

Remember… The derivative of every constant is zero!!

Function

Great Job!

Next Question

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

Power

Try Again!

Function

Great Job!

Next Question

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

Power

Try Again!

Function

Great Job!

Next Question

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 Job!

Next Question

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 Job!

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!

End Quiz

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