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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' …

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

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

Usually, the only way to differentiate a composite function is using the chain rule. If we don't recognize that a function is composite and that the chain rule must be applied, we will not be …

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.

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 …