What are Derivatives? Basics of Derivatives.

Calculus Tutorial

What are Derivatives? Basics of Derivatives.


Derivatives are something heavily used in Calculus. They are used to find the slope of the tangent line of a specific function. There are many different rules for deriving a function but I’m just going to go over a few of them. In this tutorial I’ll cover the basics.
First and foremost are constants. If you’re unaware, a constant is a number that won’t change no matter what the variable is, so basically a number. When deriving a constant, the derivative is always zero.
Secondly are variables without powers such as x. If the variable is alone then the derivative is 1. If it is not then it is whatever the constant is such as 6x becoming just 6.
Lastly for now are powers, such as x^2, x^3, so on and so forth, and this is including radicals because in calculus you’ll want to think of the radical as a power of one divided by whatever the radical is like a cubed root is 1/3. For powers you take the current power like x^2 multiply it to the constant, which in this case would be one, by the exponent and then subtract one from the power. So, x^2 would become simply 2x. In the case of radicals, you have the square root of x which is really x^1/2. You do the exact same as a regular power which makes it (x^-1/2)/2. Got me so far? Alright then, we’ll try a sample problem.

Sample Problem

Find the derivative of 3x^4






1)First and foremost you want to take a look and see if you have an exponent. In this case and scenario, you do and it’s 4.
2)Now that you’ve identified that four is your exponent you take the four and multiply it to the constant, 3. This makes it so far, 12x^4
3)After you’ve done that you subtract one from the exponent, bringing you to your final answer, 12x^3
4)Now this is the final answer I put in the multiple choice. However, this extra step is for those who are going to be doing any calculus exam or homework in the future. When you start your problem you’ll want to say d/dx 3x^4 = and then do your work. What this basically is saying is “The derivative of three x to the fourth is…” and it’s usually a mandatory requirement in any of your answers.

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I've taken up to Calculus 2 concerning math, even though I dropped the class after realizing I didn't need it. However, I did take and complete Calculus 1 with a 3.7. With science, I did do AP Biology in High School and have yet to do Human Anatomy and Physiology yet but plan to do this Fall. I have...
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