2. y = 2x ­ 1
Derivative of a Linear Function
If f(x) = mx + b where m and b are constants,
then the derivative of f is f '(x) = m

3. y = 4
Derivative of a Constant Function
If f(x) = c, where c is a constant, then
f '(x) = 0

4. Function Derivative
f(x) = x0 f '(x) = 0
f(x) = x f '(x) = 1
f(x) = x2 f '(x) = 2x
What if the exponent is negative?
eg. f(x) = x­1

5. 1 ­ 1
d 1) lim x
( x + h
dx x = h 0
h

6. The Power Rule
If n is any real number, then
d (xn) = nxn ­ 1
f '(x) =
dx

7. Using the Power rule find the derivative for each of the
following functions:
y = x2 + x­5 s = t3/4 ­ t­3
dy ds
dx dt

8. The Constant Multiple Rule
If c is any constant and f is a differentiable function,
then . .
d [c f(x)] = c f '(x)
dx
Function Derivative
y = 4 x2 f ' (x) =
f(x) = ­2x­2 f ' (x) =

9. The Sum and Difference Rule
d [f(x) + g(x)] = f '(x) + g '(x)
dx
d [f(x) ­ g(x)] = f '(x) ­ g '(x)
dx
Given the function: f(x) = 3x4 + 2x3 ­ 3x2 + 9
Find f '(x)

10. f(x) = 3x4 + 2x3 ­ 3x2 + 9
d (3x4 + 2x3 ­ 3x2 + 9)
dx

11. Exercise 4.1
Odd questions
1 ­ 19