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!

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.

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' …

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

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.

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.

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 …

Finding the derivative explicitly is a two-step process: (1) find y in terms of x, and (2) differentiate, which gives us dy/dx in terms of x. Finding the derivative implicitly is also two steps: (1) …

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, …