Derivative (Trig Function) Game
Memorizing these six basic derivative rules is essential for calculus. Scroll down the page for a more detailed explanation.
 

 
In this game, you will need to find the derivative of Trig functions using the Trig derivative rules and other 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.
 

Trig Derivative Challenge

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Find the Derivative

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How to Play the Derivative (Trig Function) Game
The game will show you a function. Your task is to differentiate the trig 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.
    
   

The Trig Function
Memorizing these six basic derivative rules is essential for calculus.
\(f(x)=\sin(x)\)
\(f’(x)=\cos(x)\)
Mnemonic Tip: S-C (Sine to Cosine)

\(f(x)=\cos(x)\)
\(f’(x)=-\sin(x)\)
Mnemonic Tip: Co-functions (cos, cot, csc always yield a negative derivative.

\(f(x)=\tan(x\)
\(f’(x)=\sec^2(x)\)
Mnemonic Tip: Tangent goes to Secant squared.

\(f(x)\cot(x)\)
\(f’(x)=-\csc^2(x)\)
Mnemonic Tip: Co-function \(\rightarrow\) Negative. Cotangent goes to Cosecant squared.

\(f(x)=\sec(x)\)
\(f’(x)=\sec(x) \tan(x)\)
Mnemonic Tip: Secant finds itself and tangent.

\(f(x)=\csc(x)\)
\(f’(x)=-\csc(x) \cot(x)\)
Mnemonic Tip: Co-function \(\rightarrow\) Negative. Cosecant finds itself and cotangent.

The Chain Rule for Composite Functions
If the argument of the trig function is not just \(x\) (e.g., \(\sin(x^2)\) or \(\cos(3x)\)), you must use the Chain Rule.
The Chain Rule states: \(\frac{d}{dx}[f(g(x))] = f’(g(x)) \cdot g’(x)\)
Example: Finding the derivative of \(y = \sin(x^2)\)
Outer Function \(f: \sin(u)\)
Inner Function \(g: u = x^2\)
\(y’ = \frac{d}{du}[\sin(u)] \cdot \frac{d}{dx}[x^2]\)
\(y’ = (\cos(u)) \cdot (2x)\)
Substitute \(u = x^2\) back in:
\(y’ = 2x \cos(x^2)\)
 

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