Use the limit definition to find the derivative of the function. f(x)=(1)/(x+2)

Name: Problem 37, Chapter 2: Calculus an Applied Approach
Uploaded: 2021-08-14T13:54:52-08:00
Duration: 3 min 9 s
Channel: Kayla Ashcroft
Description: Use the limit definition to find the derivative of the function. f(x)=(1)/(x+2)

step 1 Problem number 37 is a problem that requires us to use the limit definition of the derivative to

Use the limit definition to find the derivative of the...

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

Rational Functions Differentiation

Differentiating rational functions using the limit definition requires careful handling of fractions and ensuring proper simplification of complex expressions. This concept emphasizes the need to manage intricacies inherent in ratios of polynomials to accurately compute the derivative.

Algebraic Manipulation

Algebraic manipulation involves rearranging and simplifying expressions to facilitate the computation of limits. In the process of finding a derivative using the limit definition, it often requires combining terms, factoring, or rationalizing expressions to eliminate the variable that approaches zero, especially in the context of rational functions.

Limit Definition of the Derivative

This concept is the foundation of differential calculus, where the derivative of a function is defined as the limit of the difference quotient (f(x+h) - f(x)) / h as h approaches zero. It represents the instantaneous rate of change of the function and the slope of the tangent line at a point.

Difference Quotient

The difference quotient, (f(x+h) - f(x)) / h, is an expression that computes the average rate of change of a function over a small interval. As the interval's width approaches zero, this expression converges to the derivative at that point, illustrating the transition from average to instantaneous change.

Transcript

Please give Ace some feedback