Derivative Rules
Trig Derivatives
Components of the Derivative
Determine if a function is increasing, decreasing, or neither
Calculus Fun Facts
100
What is the product rule given h(x)=f(x)g(x)
h'(x) = f'(x)g(x)+g'(x)f(x)
or h'(x)=2*1' + 1*2
100
Derivative of sinx
cosx
100
What does the graph of the derivative describe?
It plots all the slopes of lines tangent to the original graph
100
Find the intervals where f(x) is decreasing
f(x) is decreasing in the interval (-7,3)
*Even thought at f'(-4)=0, on either side of x=-4 the f'(x) is negative, so f(x) is decreasing.
200
What is the quotient rule given h(x)=f(x)/g(x)?
(g*f'-f*g')/(g^2)
200
Derivative of tanx
sec2x
200
How do you find a critical number?
Set the derivative to 0 and solve
200
Is f(x) increasing, decreasing, or neither at f(10)?
f(x) is increasing at x=10 because f'(10)=positive #
200
Who is credited with inventing calculus?
Newton
300
What is the derivative of e^x?
e^x
300
Derivative of cscx
-cscxcotx
300
How do you decided whether a critical point is a maximum or minimum? (Hint: think sign charts!)
Positive to negative = max; negative to positive =min
300
Is f(x) increasing, decreasing, or neither at f(2)?
f(x) is decreasing at x=2, because f'(2)=negative #
300
What are the two main topics in calculus?
Derivatives and Integrals
400
What is the derivative of ln(x)?
1/x
400
Derivative of cos(x)
-sin(x)
400
To find out if f5(2) is increasing or decreasing at x=2. What do I need to know?
I need to know if f6(2) is a positive or negative number
400
Is f(x) increasing, decreasing, or neither f(-7)?
Neither, because f'(-7)=0
400
What is the first topic studied in calculus?
limits
500
Write the rule for the derivative of h(x)= f(g(x))
h'(x)=f'(g(x))*g'(x). or
h'(x) = outside' * inside'
500
Derivative of sec(x)
sec(x)tan(x)
500
Given the graph of f'(x), how do you know when the original function, f(x), is increasing?
When the graph of f'(x) is above the x-axis when is when f'(x)>0.
500
Where would you plot f'(4)=0 on the graph of f'(x)?
f'(4)=0 would be on the x-axis on the point (4,0)
500
How many kids does Ortiz-Tello have?
2