There are 7 methods we'll cover in this article for how to evaluate a derivative:
- Constant Rule
- Power Rule
- Coefficient Rule
- Sum Rule
- Difference Rule
- Derivatives you should memorize
We'll start with the easiest derivative you'll face.
If we're faced with taking the derivative of a constant, "a", it will equal 0.
The derivative of any constant is zero.
For example, if you're asked to take the derivative of 3...
...it equals 0!
Oftentimes in calculus, we'll be working with taking the derivative of polynomials (ex: x2, 3y4, etc.). The power rule is to be used with those polynomials!
The power rule only works on polynomials, a.k.a. variables with an exponent! (ex: x2, 3y4, etc.)
With f(x) = xn, we can use the following template to apply the power rule (and in-turn, take the derivative of f(x)!):
For example, if we needed to take the derivative of the following function…
…where n = 3...
...we’d solve for the derivative like so:
Letting "a" be a coefficient (a.k.a. a number without variables), we can say that…
What this says is if we multiply any of our functions by a constant, we can just bring the constant out in front of the derivative operator and focus on taking the derivative of the function itself. This makes our lives way easier... just don’t forget to add back in the constant!!!!
When taking the derivative of a term with a coefficient, pull the coefficient out in front and taking the derivative of the term like normal!
For example, if we were given the following function to take the derivative of...