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4.
1. The equation of the slope of a line, found by taking the limit as "h" approches 0 of the quantity "f(x + h) - f(x)" devided by "h." It was developed simultaniously by two european guys with funny names.

2. One of the few torture devices still in common use in "civilization."
1. If "f(x)" = "y" = "x^2 + 5x + 3" then it's derivative, "f'(x)" or "dy/dx" is "2x + 5"

2. Fuck my math teacher, if he gives us any more calculus homework I am going to diferentiate my foot up his ass!
by His holyness, Pope John Paul II December 14, 2003
 
1.
1. In calculus, the slope of a function at a point. It is found by taking the limit of (f(x + h) - f(x)) / ((x + h) - x) where h (also seen as delta x) approaches 0.

Notations for a derivative include dy/dx and f'(x) (f prime of x)

2. The mathematical incarnation of Satan Himself
1.
f(x) = 3x^3 - 4x^2 + 2x -6 //function
f'(x) = 9x^2 - 8x + 2 //first derivative
f''(x) = 18x - 8 //second derivative
f'''(x) = 18 //third derivative

2. Teacher: Today, we're going to do derivatives
Math book, as ceiling clouds over and turns red: MAY THE DEMONIC ARMIES OF HELL MARCH ACROSS YOUR MORTAL PLANE, CREATION CHAOS AND DESTRUCTION AND DRINKING THE BLOOD OF THE INNOCENT AND-
Math teacher: Change of plans! We're going to rock out to Zeppelin and have a LAN party on the school's sweet new laptops for the next hour!
Students: Hooray!
by Mr. T March 28, 2004
 
2.
Why I'm failing AP Calculus right now.
Quiz: Find the derivatives of the following.

#1: e^(-2coscsc4x)(4pitan/-7secx)^cos6x.

Me: *blank stare*
by Sid Barrett November 19, 2008
 
3.
Note: This definition of derivative is alternate to the mathematical type of derivative.

Along the lines of an integral but much more common. To take a derivative, take something that does something and do what it does back to that same thing. For clarity see examples.
A: I just took a derivative by cutting a knife.
B: Well I just took a derivative by taking a picture of a camera.
C(Math Major): What the hell are you two talking about?
by Deriffirmitive May 16, 2009
 
5.
Not original, over-used.
Donatello from Ninja Turtles, "Too derivative"

Yo, that old navy shirt is too derivative. It's one solid color with a horizontal line of another color.
by Bruce April 11, 2005
 
6.
Term used by musical elitists to down bands for having any arbitrary similarities to any bands from yesteryear. Frequently used in the comments section of music videos hosted on YouTube by people who have nothing better to do in their lives than argue on the interweb
ZOMG YOU ACTUALLY LIKE INTERPOL?!?!!1? THEY'RE SOOOOOO DERIVATIVE. I MEAN C'MON, THEY TOOOOOOOOTALLY SOUND EXACTLY LIKE JOY DIVISION EXCEPT FOR THE FACT THAT JOY DIVISION IS AUTOMATICALLY BETTER BECAUSE THEY CAME FIRST.
by I love JD too so STFU already December 12, 2008