Derivatives
Definitions
Integrals
Theorems / Formulas
Chain Rule
100
e^x
What is e^x?
100
A line that coincides with the function at one point
What is tangent line?
100
sec (x)
What is sec (x) tan (x) + c?
100
F(b) - F(a)
What is Fundamental Theorem of Calculus?
100
f(x)=sin(5x) Find dy/dx
What is 5cos(5x)
200
(3x^2) / (x^3)
What is ln (x^3)?
200
The highest value of a function over a specified domain
What is Absolute Maximum?
200
Velocity
What is acceleration?
200
f'(c) = (f(a)-f(b))/(a-b) for some c in (a,b)
What is the Mean Value Theorem?
200
f(x)= (2x^3 +7)^6 Find f'(x)?
What is 6(2x^3 +7)^5 (6x)^2
300
-2csc^2(x)
What is cot (2x)?
300
The anti-differentiation of a function
What is Integration?
300
3^x
What is 3^x / ln 3 + c?
300
If k is between f(a) and f(b), then there exists a c in [a,b] such that f(c)=k
What is the Intermediate Value Theorem?
300
f(x)= ln (3x+5) Find f'(x)
What is 3/(3x+5)
400
(4^x)ln(4)
What is 4^x?
400
The value of x that makes f'(x) = 0 or DNE
What is a critical number?
400
arc sec (2x)
What is 1 / x sqrt(4x^2-1) + c?
400
If f(a)=f(b) then f'(c)=0 for some c in (a,b)
What is Rolles Theorem?
400
g(x)= sin^2 (x) Find g'(x)
What is 2sin(x)cos(x)
500
3 / -sqrt(1-9x^2)
What is arc cos (3x)?
500
A synonym of "orthagonal"
What is perpendicular?
500
-csc (x)
What is ln |csc (x) + cot (x)| + c?
500
If lim f'(x)/g'(x)=L, then lim f(x)/g(x)=lim f'(x)/g'(x)=L.
What is L'Hopital's Rule
500
f(x)= xe^2x Find f'(x)
What is e^2x + 2xe^2x
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