The Differentiation Rules

Shortcuts for what you can already do by hand.

10 problems · about 22 minutes · FUN-3.A, FUN-3.B, FUN-3.C

NameDate

Figure — use these to answer the problems

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

y = 1x³ − 3x + 0

b-3

Point of tangency1

Figure 1

From earlier lessons. Loosen up before the new work.

2 problems

From “Differentiability”
y = |x − 2|. At which x is the derivative undefined?
Answer
From “The Derivative as a Function”
f(x) = x². What is f′(10)?
Answer

Straightforward practice. Get the method working first.

4 problems

f(x) = x⁶. Coefficient in f′(x) = ?x⁵?
Answer
4
What does the chain rule handle?
- A function inside another function.
- Two functions multiplied.
f(x) = x⁴. Coefficient in f′(x) = ?x³?
Answer
f(x) = x³, f′(x) = 3x². What is f′(3)?
Answer

The same ideas with more to keep track of.

2 problems

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

2 problems