Derivative Rules Game
Derivative rules are formulas used to find the derivative of a function, with common rules including the Power Rule, the Constant Rule, the Sum/Difference Rule for adding or subtracting functions, and the Product and Quotient Rules for multiplication and division. The Chain Rule is used for composite functions, and the rules for trigonometric and exponential functions are also frequently applied. Scroll down the page for a more detailed explanation.
 
In this game, you will need to find the derivative of a function using the derivative 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.
 

Derivative Master

Progress Score: 0

Find the Derivative

Hint: Use the Power Rule

Next Problem ➜

 

How to Play the Derivative Rules Game
The game will show you a 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 function.
   
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
Constant Rule:
The derivative of a constant \(c\) is \(0\).
\(f(x)=c\implies f^{\prime }(x)=0\)
Constant Multiple Rule:
The derivative of a constant multiplied by a function is the constant times the derivative of the function.
\(g(x)=c\cdot f(x)\implies g^{\prime }(x)=c\cdot f^{\prime }(x)\)
Power Rule:
The derivative of \(x^{n}\) is \(nx^{n-1}\).
\(f(x)=x^{n}\implies f^{\prime }(x)=nx^{n-1}\)
Sum and Difference Rules:
The derivative of a sum or difference of two functions is the sum or difference of their derivatives.
\(h(x)=f(x)\pm g(x)\implies h^{\prime }(x)=f^{\prime }(x)\pm g^{\prime }(x)\)

Product and Quotient Rules
Product Rule:
The derivative of a product of two functions is the first function times the derivative of the second, plus the second function times the derivative of the first.
\(f(x)=u(x)v(x)\implies f^{\prime }(x)=u^{\prime }(x)v(x)+u(x)v^{\prime }(x)\)
Quotient Rule:
The derivative of a quotient of two functions is given by the formula:
\(f(x)=\frac{f(x)}{g(x)}\implies f^{\prime }(x)=\frac{f^{\prime }(x)g(x)-g^{\prime }(x)f(x)}{[g(x)]^{2}}\)

Other Important Rules
Chain Rule:
Used for composite functions, it states that the derivative of \(f(g(x))\) is \(f^{\prime }(g(x))g^{\prime }(x)\).
Trigonometric Function Rules:
\(f(x)=\sin (x)\implies f^{\prime }(x)=\cos (x)\)
\(f(x)=\cos (x)\implies f^{\prime }(x)=-\sin (x)\)
\(f(x)=\tan (x)\implies f^{\prime }(x)=\sec ^{2}(x)\)
Exponential and Logarithmic Rules:
\(f(x)=e^{x}\implies f^{\prime }(x)=e^{x}\)
\(f(x)=a^{x}\implies f^{\prime }(x)=a^{x}\ln (a)\)
\(f(x)=\ln (x)\implies f^{\prime }(x)=\frac{1}{x}\)
 

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

• 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.

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