Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

AP Calculus AB · Chapter 3 · Lesson 1

Practice Worksheet

Power, Product, and Quotient Rules

Differentiating without the limit each time.

11 problems · about 24 minutes · AP Calculus AB 2.5, 2.8, 2.9

NameDate

Figure — use these to answer the problems

The tangent slope at each point is what the rules compute.

y = 1x³ − 3x + 0

Point(1, -2)
Slope of the tangent0

a1

b-3

c0

Point of tangency1

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

f(x) = x³. f'(3)?
Answer
f(x) = x⁵. f'(1)?
Answer
f(x) = 3x². f'(2)?
Answer
f(x) = x⁻¹. The derivative is −x⁻². What is f'(1)?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

5
Match each rule to its formula.
Draw a line from each item on the left to its match on the right.
- Power rule
- Product rule
- Quotient rule
- n·xⁿ⁻¹
- f'g + fg'
- (f'g − fg') / g²
f(x) = x² + x³. f'(1)?
Answer
Is (fg)' equal to f'g'? 1 for yes, 0 for no.
Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

f(x) = 10x. f'(4)?
Answer
f(x) = x⁷. f'(1)?
Answer
The Power Rule
f(x) = x⁶. What is the coefficient in the derivative?
Answer
Evaluated
f(x) = x⁴. What is f'(2)?
Answer