Derivatives Game
The Power Rule, Sum Rule, Difference Rule, and Constant Multiple Rule, allow you to find the derivative of any polynomial function f(x) instantly. Scroll down the page for a more detailed explanation.
 
In this game, you will need to find the derivative of a polynomial function using only the Power, Sum, Difference, and Constant Multiple rules. Select one of the four possible answers. The correct answer will be highlighted in green. It includes a scoring system, and clear feedback to help you master this skill.
 

How to Play the Derivatives Game
The game will show you a polynomial function. Your task is to differentiate the function and select the correct answer.
Here’s how to play:

1. Start: Each Quiz consists of 10 questions. Click “Start Game”.
   
2. Look at the Problem: You will be given a polynomial.
   
3. Select Your Answer: Select the correct derivative.br>
4. Check Your Work: Click “Submit Selection”. The game will tell you if you’re correct. If you are wrong, the correct answer will be highlighted in green.
   
5. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
6. Finish Game When you have completed 10 questions, click “Finish Game” to get your final score.
    
   

Basic Rules of Differentiation
1. The Power Rule (for individual terms)
The Power Rule is the most fundamental and applies to any single term of the form \(x^n\) (or \(ax^{n-1}\)).
The Rule:
If \(f(x) = x^n\), where n is any real number, then the derivative \(f’(x)\) is:
\(f’(x) = n \cdot x^{n-1}\)
In simple terms, you “bring the exponent down” and multiply it by the coefficient, and then subtract 1 from the exponent.
 
2. The Sum and Difference Rules (for combining terms)
The Sum and Difference Rules state that when differentiating a function made up of multiple terms added or subtracted together, you can simply differentiate each term separately and then add or subtract the results.
The Rule:
If \(f(x) = g(x) \pm h(x)\), then the derivative \(f’(x)\) is:
\(f’(x) = g’(x) \pm h’(x)\)
This rule is what allows you to differentiate entire polynomials, such as \(f(x) = 3x^2 + 5x - 8\)
Differentiate \(3x^2\), then \(5x\), and then \(-8\), and combine the results.
 

This video gives a clear, step-by-step approach to learn how to find the derivative of a polynomial.

• Show Video

Derivative Challenge (Polynomials)
Find the derivatives of polynomials using the Power, Sum, Difference, and Constant Multiple rules.

Derivative Challenge (Binomials)
Find the derivatives of the product two binomial functions. Either use the Product Rule or multiply the two binomials first to get a single polynomial and use the Power Rule.

Derivative Challenge (Product Rule)
Find the derivatives of the product a polynomial and a trig function. Use the Product Rule.

Derivative Challenge (Quotient Rule)
Find the derivatives of a function using the Quotient Rule.

Derivative Challenge (Chain Rule)
Find the derivatives of a function using the Chain Rule.

Derivative Rules
Find the derivatives of a function using the Power Rule, Constant Rule, Sum/Difference Rule, Product Rule, Quotient Rule, Chain Rule, and the rules for trigonometric and exponential functions.

Derivative Challenge (Trig Function)
Find the derivatives of Trigonometric Functions. May require other basic rules for example the Chain Rule, Product Rule etc.

Derivative Challenge (Exp, Log)
Find the derivatives of Exponential and Logarithmic Functions. May require other basic rules for example the Chain Rule, Product Rule etc.

Derivative Challenge (Hyperbolic)
Find the derivatives of Hyperbolic Functions. May require other basic rules for example the Chain Rule, Product Rule etc.

Try out our new and fun Fraction Concoction Game.

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