2. Given f(x) = x3 g(x) = x5
.
Find f '(x) g '(x) f '(x) = 3x2 g '(x) = 5x4

3. The Product Rule
. .
d [f(x) g(x)] = f(x) g '(x) + g(x) f '(x)
.
dx

4. 2 3
Find the derivative of f(x) = (x + 2) (x ­ 3)
1) Use the product rule

5. 2 3
Find the derivative of f(x) = (x + 2) (x ­ 3)
2) Multiply then differentiate

6. Quotient Rule
q(x) = f(x)
g(x)
g(x) . q(x) = f(x)

7. The Quotient Rule
d [ f(x) ] . .
g(x) f '(x) ­ f(x) g '(x)
=
dx g(x)
[g(x)]2

8. Derivatives of Trigonometric Functions
Sine Function
d sin(x) cos(x)
=
dx

9. Cosine Function
d (cos x) = ­ sin(x)
dx

10. Derivatives of Trig Functions
d (sin x) = cos(x) d (csc x) = ­ cscx cotx
dx dx
d ( cos x) = ­ sin(x) d (sec x) secx tanx
=
dx dx
d (tan x) = sec2 (x) d (cot x) = ­ csc2 x
dx dx

11. Exercise 4.3
Questions 1 ­ 23
Odd numbers