Hi everyone and welcome to MathSux! In this weeks post, we will venture into Calculus for the first time! I won’t get too much into the nitty gritty explanation of what derivative are here, but instead will provide a nice overview of Derivatives Practice Questions. This post includes everything you need to know about finding the derivatives of a function including the Power Rule, Product Rule, Quotient Rule, and the Chain Rule. Below you will see examples, a Derivative Rules Cheat Sheet, and of course practice questions! I hope these quick examples help in the classroom or for that test coming up! Let me know if it helps and you want more Calculus lessons. Happy Calculating!
What is a Derivative?
We use the derivative to find the rate of change of a function with respect to a variable. You can find out more about what a derivative is and its proper notation here at mathisfun.com. Read on below for a derivative rules cheat sheet, examples, and practice problems!
Derivative Rules Cheat Sheet:
Power Rule:
The power rule is used for finding the derivative of functions that contain variables with real exponents. Note that the derivative of any lone constant number is zero.
![derivatives of functions with exponents](httpS://azmath.info/wp-content/uploads/2022/03/1647591725_966_Screen-Shot-2021-11-24-at-6.36.05-PM-1024x212.png)
Product Rule:
The product rule is used to find the derivative of two functions that are being multiplied together.
![derivatives practice questions](httpS://azmath.info/wp-content/uploads/2022/03/1647591726_794_Screen-Shot-2021-11-24-at-6.37.03-PM-1024x203.png)
Quotient Rule:
Applying the quotient rule, will find the derivative of any two functions set up as a ratio. Be sure to notice any numbers or variables in the denominator that can be brought to the numerator (if that’s the case, can use the more friendly power rule).
![derivatives of trigonometric functions](httpS://azmath.info/wp-content/uploads/2022/03/1647591727_553_Screen-Shot-2021-11-24-at-6.43.12-PM-1024x772.png)
Chain Rule:
The chain rule allows us to find the derivative of nested functions. This is great for trigonometric functions and entire functions that are raised to an exponent.
![calculus chain rule examples](httpS://azmath.info/wp-content/uploads/2022/03/1647591727_290_Screen-Shot-2021-11-24-at-6.42.15-PM-1024x265.png)
Ready for some practice questions!? Check out the ones below to test your knowledge of derivatives!
Derivatives Practice Questions:
Find the derivatives for each function below.
![Derivatives Practice Questions](httpS://azmath.info/wp-content/uploads/2022/03/1647591728_859_Screen-Shot-2021-11-24-at-7.41.50-PM-1024x115.png)
Solutions:
![](httpS://azmath.info/wp-content/uploads/2022/03/1647591728_42_Screen-Shot-2021-11-24-at-7.42.39-PM.png)
Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! ?
*Also, if you want to check out Rate of Change basics click this link here!
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