1. Differentiation Rules for Products, Quotients,
2.3
Differentiation Rules for Products, Quotients,
Secants, and Tangents

2. Product Rule
The 1st times the der. of the 2nd + the 2nd times
the der. of the 1st uv’+vu’
Ex. f(x) = (3x – 2x2)(5 + 4x)
f’(x) =
(3x – 2x2)
(4) +
(5 + 4x)
(3 – 4x)
f’(x) = 12x – 8x – 20x + 12x – 16x2
f’(x) = -24x2 + 4x + 15

3. x
cos x +
sin x
(1)
= x cos x + sin x
y = 2x cos x – 2 sin x
y’ = (2x)(-sin x)
+ cos x (2)
- 2 cos x
= -2x sin x
Quotient Rule

4. Differentiate
(2 – 3x)
(4x – 4)
- (2x2 – 4x + 3)
(-3)
y’ =
(-12x2 + 20x – 8) – (- 6x2 + 12x – 9)
y’ =
-6x2 + 8x + 1
y’ =

6. Derivatives of Trigonometric Functions
Differentiate
y = x – tan x
y = x sec x
y’ = x(sec x tan x) + (sec x)(1)
y’ = sec x(x tan x + 1)