Derivative Rules
What is the product rule?
f'g+g'f
Derivative of sinx
cosx
What does the graph of the derivative describe?
It shows all the slopes of lines tangent to the original graph
F(x)= 2x3-3x2-12x+18, when is the graph decreasing and concave up?
(-1, .5)
What is the name of that guy who made the rule about limits that are 0/0
lhopital
What is the quotient rule?
f'g-g'f/ g2
Derivative of tanx
sec2x
How do you find a critical number?
Set the derivative to 0
Find the derivative of f(g(x^2))
Who is credited with inventing calculus?
Newton
What is the derivative of e^x?
e^x
Derivative of cscx
-cscxcotx
How do you decided whether a critical point is a maximum or minimum?
Positive to negative = max; negative to positive =min
Differentiate: 3x^2 +4xy
6x+4y+4x(dy/dx)
What are the two main topics in calculus?
Derivatives and Integrals
What is the derivative of ln(x)?
1/x
Derivative of cos(x)
-sin(x)
What does it mean when f''(x)= 0
a possible inflection point
evaluate limx 3 (f(3x)-f(9))/(x-3)
f'(3x)(3) = 3f'(9)
What is the first topic studied in calculus?
limits
Write the rule for the derivative of f(g(x))
f'(g(x))g'(x)
Derivative of sec(x)
sec(x)tan(x)
How do you figure out when the original graph, f(x), is concave up?
When f''(x)>0
What does a removeable discontinuity look like on a graph?
a hole
How many kids does Mrs. Grimm have?
4