AP Calculus BC Unit 2 practice questions: Differentiation: Definition and Fundamental Properties
8 original multiple-choice questions on AP Calc BC Unit 2, differentiation: definition and fundamental properties. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 8
What is the derivative of f(x) = x·eˣ?
Question 2 of 8
If f(x) = tan x, what is f′(π/4)?
Question 3 of 8
What does lim (h→0) of [(2 + h)² − 4]/h equal?
Question 4 of 8
What is d/dx of x³ − 5x?
Question 5 of 8
What is d/dx of x/(x + 1)?
Question 6 of 8
If f(x) = ln x, what is f′(e)?
Question 7 of 8
Which statement is always true?
Question 8 of 8
What is the equation of the tangent line to y = x² at x = 3?
Key ideas in Unit 2
- The derivative is the limit of the difference quotient, [f(x + h) − f(x)]/h, and gives the instantaneous rate of change and the slope of the tangent line.
- Know the power, constant multiple, sum, product and quotient rules, plus the derivatives of sin, cos, eˣ and ln x.
- Differentiability implies continuity, but corners, cusps and vertical tangents are continuous points with no derivative.
- The tangent line at x = a is y − f(a) = f′(a)(x − a).
More AP Calc BC practice
← Unit 1: Limits and Continuity
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions →
The full AP Calculus BC practice test, all units
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