Derivative Rules
What rule is this? f'(x)g(x)+f(x)g'(x)
The Product Rule
d/dx cos(x)?
-sin(x)
d/dx ex
ex
What rule do you use when you get indeterminate form while trying to find a limit?
L'hôpital's Rule
What is the derivative of xn if n is equal to the value of the year the declaration of independence was signed?
1776x1775
What rule is this? (f'(x)g(x)-f(x)g'(x))/(g(x))2
The Quotient Rule
d/dx tan(x)?
sec2(x)
d/dx x3
3x2
What theorem is this: for any differentiable function f on an interval [a,b] (within the domain of f), there exists a number c within (a,b) such as that f'(c) is equal to the function's average rate of change over [a,b]?
Mean Value Theorem
What is the anti-derivative of nx16 if n is equal to the address of Sherlock Holmes?
13x17
What is this rule? d/dx xn=nxn-1
The Power Rule
d/dx csc(x)?
-tan(x)csc(x)
d/dx 3x4+3x
12x3+3
What Theorem is this: If a function f is continuous over the interval [a,b] (must include both values), the function will take any value between f(a) and f(b) over the interval?
The Intermediate Value Theorem
What is d/dx n*ln(x) if n is equal to the number of Star Wars movies (ALL of them).
12/x
What rule is this? f'(g(x))*g'(x)
The Chain Rule
d/dx tan-1(x)?
1/(1+x2)
d/dx 3ln(x)
3/x
What Theorem is this:
There exists a c such that
f(c) ≤ f(a) ≤ f(b) (min)
f(a) ≤ f(b) ≤ f(c) (max)
(given that f is continuous on the interval [a,b])
The Extreme Value Theorem
What is d/dx n*ex if n is equal to the year Shrek was released?
2001*ex
What is this an example of: d/dx[x²+y²=25]?
Implicit Differentiation
d/dx cot-1(x)
-1/(1+x2)
d/dx 3x2*4x
36x2
What theorem is this equation a part of: the integral of a to b f(t)dt=F(b)-F(a)?
The Fundamental Theorem of Calculus
What is d/dx xn+xn-1 if n is equal to the the number president that Herbert Hoover was?
31x30+30x29