Essentially a derivative is the slope of a given any point on a function, other wise known as the instant rate of change on the point (△y/△x).
The literal and formalized definition of the derivative is the following formula: “Visual Derivative Definition” (cr: Math Visual Proofs)
To solve problems using this formula, you will need to recall how to take the limit of a equation.
- expand f(x+h) and f(x) according to the function and points given. Keep limit notation.
- add like terms and simplify until you can cancel out a “h” from both the numerator and denominator. Keep limit notation.
- NOW TAKE THE LIMIT.
- Simplify and remaining terms/numbers.
How to use this formula? “Definition of the Derivative” (cr: Organic Chemistry Tutor)
This is a lengthy formula to memorize and use, which is why we introduce various derivative rules in the next lesson (2.2), HOWEVER do NOT disregard this lesson/practice as it will be tested on + its just nice to practice your limits!