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
What does it mean when f'(x)= 0
A maximum, minimum, or critical point
If f(x)= x2-4, and g is a differentiable function of x, what is the derivative of f(g(x))
2g'(x)
What does calculus mean in latin?
small stone
What is the derivative of ax?
ax x ln(a)
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
3xlog(3)
What's Mr. Rose's cat's name?
Scarlett
What is the derivative of logax?
1/x times 1/x
Derivative of tan-1x
1/(1+ x2)
What does it mean when f''(x)= 0
potential point of inflection
limit of the expression (e^x-cos(x))/x as x goes to 0
1
Why is the derivative of x 1?
the line y=x, the slope is always one
Write the chain rule
(f’ º g) × g’
Derivative of csc-1x
1/ (lxl ((x2-1)1/2)
How do you figure out when the original graph, f(x), is concave up?
When f''(x)>0
draw a graph, find the area geometrically with trapezoids
Is statistics real math?
no