The Derivative Function (Cont'd)

OVERVIEW:

• Alternative Notations for the Derivative
• y = nx^(n-1)
• Derive f(x) = x^3
• Derive y = -1/x

We finally finished our lessons with the topics covered in 2.3 of our Calculus: Concepts and Calculators textbook. According to yesterday's substitute's substitute, the textbook we use is the worst textbook she has ever seen in her life because it's convoluted and because its explanations can be explained better too, but that is why we have the BLOG, our online interactive textbook to help better our understanding.


Alternative Notations for the Derivative

f'(a) is the symbol used by Lagrange. E.g. If f(x) = x^2, its derivative is f'(x) = 2x.
dy/dx is the symbol used by Leibniz. E.g. If f(x) = x^2, its derivative is dy/dx = 2x.


y = nx^(n-1)

Then the Benchmeister took over the class and starting teaching us. He taught us a shortcut in finding the formula of a derivative by using a formula. We were so amazed at his genius work that probably only Dr. Eviatar and Bench can understand it, because I know I didn't. Mr. K says, "If you don't understand something in class, you can bet that six other people in that class probably didn't get it as well." So I'm counting on other people to fill in the blanks that I've left in this blog post. Also, the formula that Bench gave us is something to be taught some time in the future. Anyways, we ended up getting the formula, y = nx^(n-1).


Derive f(x) = x^3.



Derive y = -1/x.Using the y = nx^(n-1) formula,
y = nx^(n-1)
y = (-1)x^[(-1)-1]
y = -x^-2
y = -1/x^2


END NOTES:

• Homework: 2.3 The Derivative Function #1, 5, 7, 9, 11, 12, 21, 27
• Note: The principal says we won't get our laptops until he talks to Mr. K (assuming that Mr. K gets back in action at our school). Well, guess what? WE ARE THE RADICAL CALCULUS GROUP. WE WANT OUR LAPTOPS, AND WE WANT OUR LAPTOPS NOW!
  
• Next scribe is Joyce.