Let's dive into the power rule, a handy tool for finding the derivative of xⁿ. This rule simplifies the process of taking derivatives, especially for polynomials, by bringing the exponent out front …

Let's dive into the power rule, a handy tool for finding the derivative of xⁿ. This rule simplifies the process of taking derivatives, especially for polynomials, by bringing the exponent out front …

Discover how the power rule helps us find derivatives of functions like 1/x, ∛x, or ∛x². By rewriting these functions as xⁿ, where n is a negative or fractional exponent, we can apply the power …

The power rule states that the derivative of x raised to the power of n is n times x raised to the power of n-1, and this rule holds even when n is a negative integer.

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Let's explore the power rule's validity by examining the derivatives of x¹ and x². We'll analyze the slopes of tangent lines for these functions and then see how the power rule provides …

The power rule: log b (M p) = p log b (M) This property says that the log of a power is the exponent times the logarithm of the base of the power. Show me a numerical example please.

Review your knowledge of the reverse power rule for integrals and solve problems with it.

Let's take the derivative with respect to x of x to the n plus 1-th power over n plus 1 plus some constant c. And we're going to assume here, because we want this expression to be defined, …

In this lesson, we will prove three logarithm properties: the product rule, the quotient rule, and the power rule. Before we begin, let's recall a useful fact that will help us along the way.