Differentiate integer powers (mixed positive and negative) Get 3 of 4 questions to level up!

Making expressions more efficient to differentiate isn't just a matter of convenience; The simpler and shorter the differentiation, the smaller the chance that you make a mistake along the way!

How do I differentiate logarithmic functions? First, you should know the derivatives for the basic logarithmic functions: d d x ln (x) = 1 x d d x log b (x) = 1 ln (b) ⋅ x

Oct 4, 2023 · In just a few seconds, they can generate a nearly infinite range of lesson plans and learning materials. As an example, let’s look at how Khanmigo, Khan Academy’s AI teaching …

For x^ (2), we first differentiate x^ (2) with respect to x, which is 2x, and then x with respect to x, which is 1. Everytime you use the chain rule on a function solely in x, you'll get a dx/dx factor, …

In this video, we explore how to differentiate related functions. We'll use the chain rule to find the derivatives of these functions, all linked to the same variable. It's a cool way to see how …

Let's explore how to differentiate polynomials using the power rule and derivative properties. We work with the function f (x)=x⁵+2x³-x² and apply the power rule to find its derivative, f' …

You can differentiate (using the difference quotient) to prove that any arbitrary logarithm can be changed into the form, since you can always differentiate using change of base to logarithms first.

Basically an introduction to the concept that you will often need multiple rules/steps to differentiate an expression, so it's useful to think of strategies for how to do that when you see a problem …

In implicit differentiation, we differentiate each side of an equation with two variables (usually x and y ) by treating one of the variables as a function of the other.