Basic Derivative Rules/Definition of the Derivative
Position, Velocity, and Acceleration
Product Rule/Quotient Rule
Derivatives and their graphs
Chain Rule
100
What is the definition of a derivative?
lim [ f(x+h) - f(x)] / (h)
h -> 0
100
The acceleration function is the second derivative of...
position
100
What is the product rule?
[f(x)g(x)]'=f'(x)g(x)+f(x)g'(x)
100
What does the graph of a derivative represent?
The graph of a derivative represents the slope of the tangent line at every value of x in the original graph
100
When does the chain rule apply?
The chain rule applies when there is a function that is contained within another function, meaning the chain rule applies when f(g(x)).
200
What things must be true in order for differentiability rules to apply?
Function must be continuous
Graph of the function must be smooth - no corners
If f has a derivative at x = a then f is continuous at x = a
200
The position function is the integral of...
the velocity function
200
What is the quotient rule?
(f/g)′=(f′g−fg′)/(gˆ2)
(lodhi - hidlo) / (lolo)
200
What occurs to the graph of f'(x) when the graph of f(x) is positive?
f'(x) is increasing
200
What is the chain rule?
f(g(x))' = f'(g(x))⋅g'(x)
300
Name 2 of the basic differentiability rules and explain what they are
Constant Rule: The derivative of a constant is always zero
Power Rule: when the function has an exponent, in the derivative of that function you multiply the function by the exponent and subtract a power
Sum or Difference Rule: Each term should be treated separately
300
What is the acceleration function of an object if its position function is:
p(t) = 8t^5 + 20t^2 + 737t - 89128409472
a(t) = 160t^3 + 40
300
Given f(x) = (3x^2 – 1)(x^2 + 5x +2), find the derivative of f(x).
12x^3 + 45x^2 +10x - 5
300
What happens to the graph of f(x) if f''(x) is negative?
the graph of f(x) is concave downwards
300
Let f(x)=6x+3and g(x)=−2x+5. Use the chain rule to calculate h′(x), where h(x)=f(g(x))h(x).
−12x+33
400
Rewrite f(x) so that there aren't any negative exponents
f(x) = x^-4 + x^(-1/2) + x^(-3/2) + 5^-x
f(x) = (1/x^4) + (1/√x) + [1/x^(3/2)] + (1/5^x)
400
What is the acceleration function if the velocity function is:
v(t) = (t-1)/(t+2)
3/(t+2)^2
400
Given that 
, find f ‘(x)
(3x^2 + x^6)/(1 - x^4)^2
400
What happens to the graph of f(x) when f''(x) is equal to zero?
The graph of f(x) has a point of inflection
400
Find the derivative of y = x(x^4 + 9)^3
y' = 12x^4(x^4+9)^2 + (x^4+9)^3
500
Find the derivative of the function f(x)=2/x^2 using the limit definition.
-4/x^3
500
What is the the position function if the velocity function is v(t) = 1/(4-t)
p(t) = -ln|4-t| + c
500
Find the derivative of
f(x) = (x^2/x)(1/4x^3)
-1/(2x^3)
500
What are the max/min points of
f(x) = (1/3)x^3 + (3/2)x^2 - 4x
Max point at x = -4
Min point at x = -1
500
What is f´(t) if
