Find the derivative of each function. f(x)=(2)/((x^2-1)^4) |...

Name: Problem 16, Chapter 3: Applied Calculus for the Managerial, Life, and Social Sciences
Uploaded: 2021-05-04T19:16:20-08:00
Duration: 1 min 32 s
Channel: Gregory Higby
Description: Find the derivative of each function. f(x)=(2)/((x^2-1)^4)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Chain Rule

The chain rule is a fundamental differentiation technique used when dealing with composite functions. It states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. This concept is essential when differentiating functions where one function is nested inside another.

Power Rule

The power rule is a basic rule in calculus that provides a simple way to differentiate functions in the form of x raised to a constant power. It states that the derivative of x? is n*x^(n-1). This rule can also be applied to functions written with negative exponents, often used in conjunction with the chain rule when differentiating complex expressions.

Rewriting Functions for Differentiation

Often, functions are rewritten (such as expressing a reciprocal as a negative power) to make the application of differentiation rules, like the power rule and chain rule, more straightforward. This technique simplifies the differentiation process by reducing complex fractions into a form that is easier to handle mathematically.

Transcript

Please give Ace some feedback