Derivatives are a very fundamental item in calculus. They give you the slope of a line. They can be really quite handy. Today in this tutorial, I will be demonstrating how to take the derivative of a simple function.
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Step 1: Identify Different Terms of Function
The function we will be using is f(x) = 3x^3 + 8x^2 - 2x + 3
The terms of the function are the things before and after every operator. For example, the first term in our function is 3x^3. The last term is 3. Make sure you identify and separate these for later.
Step 2: Identify Exponent and Coefficient of Each Term
The exponent of each term is the superscript number. In this case, the exponent for our first term is 3. The exponent for our second to last term is 1 (if there isn't an exponent on a variable, then the exponent is just 1). Exponents on numbers don't count because you can simplify it. I would recommend doing so for any other derive problems you are given.
The coefficient of a term is defined quite literally as the number that comes directly before the variable. For example, the coefficient for our second term is 8. The coefficient of our second to last term is -2 (if you have a function like f(x) = x - 2, the second term would be -2 because there is a negative in front of it. This applies to everything).
Step 3: Math It Up
The formula for calculating derivatives goes as follows: a*cx^a-1 this is better shown in the first image above. So what we need to do for each term is multiply the coefficient by the exponent. Then subtract one from the exponent. Repeat this for each term. Just so you don't get confused, the variable in the third term of the original function should lose it's variable after taking the derivative. The last image explains why. After finishing each term, put them together in another function. And then you're done! If you did this correctly, you should have ended up with f'(x) = 9x^2 + 16x - 2