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Unit: Differentiation for physics (Prerequisite)

Gain some experience working with secant lines. This will help us on our journey to find a formal definition for the derivative.
There are two ways to define the derivative of function f at point x=a. The formal definition is the limit of [f(a+h)-f(x)]/h as h approaches 0, and the alternative definition is the limit of [f(x)-f(a)]/(x-a) as x approaches a. Make introduction with these two definitions.
This may blow your mind, but the derivative of a function is a function in itself! Get comfortable in thinking about the derivative as a function that is separate from, but tightly related to, its original function.
If you ever tried to find derivatives using their formal definition, you probably know how tedious that may be. Fortunately, we have ways for finding derivatives much quicker, using differentiation rules! Make your first steps in this fascinating world by working with the more basic rules. For example, the derivative of [f(x)+g(x)] is f'(x)+g'(x), and the derivative of k⋅f(x) is k⋅f'(x).
The power rule says that the derivative of xⁿ is n⋅xⁿ⁻¹. It allows us to quickly find the derivative of any polynomial, and it doesn't even stop there! Make introduction with this simple but powerful rule.
The derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). How convenient! Practice differentiating functions that include sine and cosine.
The product rule says that the derivative of the product f(x)g(x) is f'(x)g(x)+f(x)g'(x). This helps us find the derivative of a function which is a product of two other, more basic, functions.

About this unit

Certain ideas in physics require the prior knowledge of differentiation. The big idea of differential calculus is the concept of the derivative, which essentially gives us the rate of change of a quantity like displacement or velocity.