# Differential Calculus

Learn about the fundamentals of calculus, including limits and derivatives.

Start## Key Concepts

Review core concepts you need to learn to master this subject

Limits

Limit Definition of the Derivative

Derivative Properties

Derivatives in Python

Calculating Derivatives

Derivative Rules

Limits

Limits

Limits quantify what happens to the values of a function as we approach a given point. This can be defined notationally as:

`$\lim_{x \rightarrow 6} f(x) = L$`

We can read this in simple terms as “the limit as *x* goes to 6 of f(x) approaches some value L”.

Introduction to Differential Calculus

Lesson 1 of 1

- 1Data scientists often are asked to make data-driven recommendations on the best way to solve a problem. Along the way, they build and fit statistical models to support their claims, make predictio…
- 3Suppose we wanted to measure a runner’s instantaneous speed using a stopwatch. By instantaneous speed, we mean their speed at an exact moment in time. Let’s define
*f(t)*as the runner’s distance … - 4In the previous exercise, we discussed the idea of the derivative at a point as the instantaneous rate of change at that point. The idea behind the definition is that by finding how the function c…
- 5Derivative functions contain important information. Let’s look at a couple of examples. Going back to our running example,
*f(t)*describes a runner’s position as a function of time; therefore, the… - 6We have talked at length about derivatives abstractly. But how do we actually find derivative functions? We will outline this in this exercise and the next one. The answer is through a series of “…
- 7So we now have an idea on where to start differentiating (that is, take the derivative of) things like: \begin{aligned} 4\log(x) \ x^2 + \log(x) \ x^2\log(x) \ \end{aligned} Our final step is…
- 8We’ve discussed how to compute derivatives by hand. However, oftentimes when working on a computer, we have functions given to us in array form rather than an explicit equation. In this exercise, w…

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