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

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' …

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.

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How do I differentiate rational functions? To differentiate rational functions, all you need is to know how to differentiate polynomials and the quotient rule. Let's differentiate x 2 2 x 1 for example.

If I am asked to take the derivative of a difference of polynomials, is it safe to rewrite the problem as the derivative of the sum of negative numbers? (Excluding the first polynomial unless it's …

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.

Let's dive deeper into the fascinating world of derivatives, specifically focusing on the derivative of aˣ for any positive base a. Using the derivative of eˣ and the chain rule, we unravel the mystery …

Let's explore the concept that the derivative of ln(x) is 1/x by examining the slopes of tangent lines at various points on the graph of y=ln(x). We'll observe that the slopes match the values of 1/x, …

Oct 4, 2023 · As an example, let’s look at how Khanmigo, Khan Academy’s AI teaching assistant, can help educators quickly differentiate a grammar lesson for both advanced readers and …