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The Power Rule:
if
then f'(x) =

If f(x) = sin x then f'(x) = ?
f'(x) = cos x

if f(x) = cos x then f'(x) =
f'(x) = sin x

If f(x) = tan x then f'(x) =

If f(x) = cot x then f'(x) =

If f(x) = sec x then f'(x) =
f'(x) = sec x tan x

If f(x) = csc x then f'(x) =
f'(x) = csc x cot x

Chain Rule (composite functions)
If
then
f'(x) =
f'(x)= g'[f(x)]f'(x)

If
what is the domain?
what is f'(x)?
 Domain:

If
What is the domain?
What is f'(x)?
Domain:

If
What is the domain?
What is f'(x)?
Domain:

If
What is the domain?
What is f'(x)?
 Domain:

If
What is the domain?
at is f'(x)?

If
What is the domain?
What is f'(x)?

If
What is f'(x)?

If
; a > 0; a 1
What is f(x)?

If
What is f'(x)?

If
a > 0
a 1
What is f'(x)

What are four things derivatives are used for?
 1. curve, and sketching.
 2. solving maximum and minimum problems.
 3. related rate problems.
 4. approximating function values.

What are the (3) steps to finding the equation of the tangent line at a point?
 1. Take the derivative of f(x).
 2. Find f'(x)=y
 3. Using yy1=m(xx1) to find the equation.

Where are the critical points?
 1. where f'(x) = 0
 2. where f'(x) = does not exist.

The ______ ______ theorem states that if f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and minimum value on [a,b]
Extreme Value Theorem

The relationship between the slope of a tangent line to a curve and the secant line through points on a curve at the end points of an interval is the ______ ______ Theorem.
Mean Value

What is f'(c) defined as in the Mean Value Theorem?


