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Derivatives and Integrals
History of Calculus
Theorems
Rules
Notation
100

3x is the derivative of this function

1.5x2

100

This form of mathematics has to do with the infinitesimal, and focuses on limits, derivatives, and integrals.

Calculus

100
This theorem states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero.
What is Rolle's Theorem
100

What is the product rule? 

f'(g(x)) * g'(x)

100
dy/dx is the notation for this commonly used calculus operation.
What is a derivative
200

The derivative of (1/2)x3

(3/2)x2

200

This historical genius is known to have discovered Calculus AND gravity 

Isaac Newton

200
The theorem used to evaluate a definite integral of a function - perhaps the most important theorem in Calculus, giving it this appropriate name.
What is the 1st Fundamental Theorem of Calculus
200

You would need this rule to get the derivative of the function f(x) = sin(5x+3)

What is the Chain Rule

200
The "S" commonly used in integral notation stands for this
What is sum
300

The function tan(x) is not continuous everywhere because it has what behavior?

Vertical tangent lines OR Asymptotes

300

This man, whose name translates to "hospital" is known for coming up with a calculus rule named after him.

L'Hôpital

300
This theorem is also known as "Rolle's Theorem Turned on its Side"
What is the Mean Value Theorem
300

What is the constant multiple rule? 

d/dx ( c (f(x)) = c (d/dx f(x))

300
The Greek letter Epsilon represents this
What is an extremely small positive number
400

-cos(x) is the derivative of an equation. The antiderivative of -cos(x) is: 

-sin(x) + C

400
This man is known for shouting "Eureka!" when he discovered he could measure volume by water displacement.
Who is Euler
400
This theorem allows us to calculate the limit of sin(x)/x as x approaches zero.
What is the Squeeze Theorem
400
This function is the only function which is its own derivative.
What is e^x
400
What is the greek symbol Sigma used for in mathematics?
What is summation/summation notation
500

The derivative of  4x2 - 3ex

8x - 3ex

500
The biggest controversy over who invented calculus is between these two people.
Who are Isaac Newton and Godfried Leibniz
500
This theorem is named after the best calculus teacher in the history of mankind.
What is Green's Theorem
500

What is the quotient rule?

What is (f'(x)g(x)-g'(x)f(x))/(g(x)^2)

500
A y with a dot above it was Newton's notation stands for this
What is the derivative of y