Unit 2: Differentiation: Definition and Basic Derivative Rules

AP Calculus AB — 8 practice questions with detailed explanations. Use the links below to open each full question page (ideal for search indexing and deep study).

Unit summary

This unit covers core ideas tested on the AP exam. Each listed item links to a standalone page with the full stem, answer choices where applicable, a step-by-step explanation, and the correct answer. Difficulty labels help you prioritize review.

Questions in this unit

Sample prompts

Short previews of topics covered (not full question text).

The temperature $T$ of a cup of coffee, in degrees Fahrenheit, is modeled by $T(…
Let $y = (4x^3 - 7)^8$. What is $\frac{dy}{dx}$?…
If $g(\theta) = \sec(\theta) + \csc(\theta)$, what is $g'(\theta)$?…
What is the derivative of $f(x) = \frac{5x+1}{x^2-4}$?…
If $h(x) = x^3 \sin(x)$, what is the value of $h'(\pi)$?…
For $x \neq 0$, what is the derivative of $y = \frac{x^4 - 3x^2 + 5}{x^2}$?…
Let $f(x)$ be a piecewise function defined as $f(x) = \begin{cases} x^2 - 1 &\te…
Let $f$ be a function for which $\lim_{h \to 0} \frac{f(3+h) - f(3)}{h} = -4$. W…