Derivative quiz: practice rules and sharpen your calculus skills
Quick, free derivative rules quiz. Instant results.
Editorial: Review CompletedUpdated Aug 27, 2025
This derivative quiz helps you practice power, product, quotient, and chain rules while building speed and accuracy. Answer 20 quick questions and get instant results to spot mistakes and review steps. For more practice, take our calculus quiz, try a focused differentiation practice test, or warm up with AP calculus unit 1 practice.
Study Outcomes
- Understand the fundamental concept of the derivative and its geometric interpretation.
- Compute derivatives for various functions using established differentiation rules.
- Apply differentiation techniques to solve practical calculus problems.
- Analyze function behavior by identifying critical points and rates of change.
- Evaluate problem-solving strategies to enhance test and exam preparation.
Derivative Practice Cheat Sheet
- Master the Power Rule - To differentiate x❿, multiply by the exponent and reduce the power by one: d/dx(x❿) = n·x❿❻¹. For instance, d/dx(x³) = 3x². It feels like a magic trick that makes tackling polynomials instantaneously easier!
- Sum & Difference Rules - Breaking down complex expressions is a snap since d/dx[f(x) ± g(x)] = f′(x) ± g′(x). You simply differentiate each term separately and keep the plus or minus sign. It's as satisfying as assembling building blocks one piece at a time!
- Utilize the Product Rule - When two functions u(x) and v(x) are multiplied, use d/dx[u·v] = u′·v + u·v′. This handy formula ensures you don't miss a beat when products pop up. Think of it as juggling two balls - keep both in motion with the right rhythm!
- Understand the Quotient Rule - For a fraction u(x)/v(x), apply d/dx[u/v] = [u′·v - u·v′] / v². It may look complex, but it's a straightforward subtraction and division routine. Just remember "low d‑high minus high d‑low, over low squared" to ace any fraction!
- Grasp the Chain Rule - Composite functions f(g(x)) use d/dx[f∘g] = f′(g(x))·g′(x). You peel back each layer like an onion, differentiating the outer function then plunging into the inner one. It's your go‑to move for nested formulas!
- Differentiate Trigonometric Functions - Memorize that d/dx[sin(x)] = cos(x) and d/dx[cos(x)] = - sin(x). Once you lock in these basics, every other trig derivative is a piece of cake. Who knew circles and waves could be so friendly?
- Differentiate Exponential Functions - Exponentials are your allies: d/dx[eˣ] = eˣ. That means the function and its derivative are identical - talk about effortless growth! It's like having an endless energy boost in calculus form.
- Differentiate Logarithmic Functions - For natural logs, d/dx[ln(x)] = 1/x. It's the neat inverse of exponentials and saves you every time you see ln popping up. Just remember the reciprocal trick and you're golden!
- Apply the Constant Multiple Rule - If you have a constant c times a function, d/dx[c·f(x)] = c·f′(x). The constant tags along happily while you do the real work on f(x). It's the ultimate shortcut for scaling derivatives!
- Practice with Real-World Applications - Use these rules to solve rate‑of‑change problems in physics, biology, and economics. Whether you're finding velocity from position or analyzing growth trends, hands‑on practice cements your skills. Grab some real data and watch calculus come to life!
