Derivatives
The derivative of
y = 3x^2 + 4x - 7
What is 6x + 4 ?
It is the formula for finding the distance between two points A(x, y) and B(3, -4)
What is
sqrt((x-3)^2 + (y+4)^2)
?
It is the result when you get when you integrate
int1dx
What is x + C ?
He is 8 years old, furry, and diabetic
Who is Ms. Brown's cat, Carson?
lim_(x->oo) 1/x
What is 0 ?
The derivative of f(x) = cos x
What is -sin x ?
The formula for finding the volume of a right circular cylinder.
What is
pir^2h
It is the result when you get when you integrate
inte^xdx
What is
e^x + C
?
It is the answer to life the universe and everything.
What is 42?
lim_(x->0)(cos x - 1) / x
What is 0 ?
The derivative of y = sec x
What is sec x tan x ?
It is
lim_(h->0) (f(x+h)-f(x))/h
What is the definition of a derivative?
It is the result when you get when you integrate
int1/x dx
What is ln |x| + C ?
They mean the same thing
y'
dy/dx
What is a derivative?
lim_(x->0)sinx/(2x)
What is 1/2 ?
The derivative of
f(x) = a^x
What is
(ln a) a^x
?
It is
lim_(x->a)(f(x)-f(a))/(x-a)
What is the definition of the average rate of change?
It is the result when you get when you integrate
intsec^2 x dx
What is tan x + C ?
It's what your AB teacher seared into your brain using an extreme trauma.
What is the quotient rule?
lim_(h->0)(e^h - 1) / h
What is 1 ?
The derivative of
f(x) = tan^(-1)x
What is
1 / (1 + x^2)
?
It is
1/(b-a)int_a^bf(x)dx
What is the average value of a function from a to b?
It is the result when you get when you integrate
inttan x dx
What is ln |sec x| + C ?
OR
What is -ln |cos x| + C ?
The rule that allows us to do this:
d/(dt)[f(x)] = f'(x)*dx/dt
What is the Chain Rule ?
This is a special number
lim_(x->oo)(1 + (1/x))^x
What is e ?