1. The Constant Rule m = 0 The derivative of a constant function is 0.
I don’t even have to think too hard to do that.
m = 0
The derivative of a constant function is 0.

2. The Power Rule That was easy
If n is a rational number, then the function f(x) = xn is differentiable.
That was easy

3. The Constant Multiple Rule
If f is a differentiable function and c is a real number, cf is also differentiable.
These are the easy ones. Let’s try some more difficult problems.
I knew that was coming.

4. Constant Multiple Examples

5. Homework
Page 115: 25 – 30 All

6. Sum and Difference Rule
The derivative of the sum, or difference, of two differentiable functions is differentiable and is the sum, or difference of their derivatives.

7. Derivative of Sine and Cosine

8. Sine and Cosine Examples

9. Homework
Page 115: 4 – 24
Even Numbers

10. Finding an Equation of a Tangent Line
Find an equation of the tangent line to the graph of f(x) = x2 when x = –1
f(x) = x2
First find the point of tangency at x = -1
The point of tangency is
Next, find the derivative of f(x) = x2
y = -2x - 1
Therefore, the slope of the tangent line at x = –1 is
We now have a point on the line and the slope, so use the point-slope form to find the equation of the tangent line.

11. Graphs of Derivatives Since f is cubic, f’ is quadratic.
Compare the graph of the following function with the graph of it’s derivative.
Since f is cubic, f’ is quadratic.
f increases, f’ is positive.
Let’s look at another example.
f decreases, f’ is negative.
f increases, f’ is positive.
I think I can see the pattern.

12. Graph of Sine and its Derivative
Increasing
Decreasing
Negative
Negative
Positive
Increasing
Decreasing
Positive
I get the picture. This is pretty easy.

13. Comparing a Function and its Derivative
In each of the following, determine which is the function, f and which is the derivative, f’, and explain your answer. f f f f’ f’ f’
f is quadratic f’ is linear
f is cubic
f’ is quadratic
f is linear
f’ is constant
When f decreases
f’ is negative
f constantly decreases
f’ is always negative
f constantly increases
f’ is always positive
When f increases
f’ is positive
That was easy

14. Graphs of Derivatives Worksheet
Homework
Graphs of Derivatives Worksheet