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