Find f^'(a). f(x)=x^-2

Name: Problem 30, Chapter 2: Calculus
Uploaded: 2021-08-26T00:50:00-08:00
Channel: David Mccaslin
Description: Find f^'(a). f(x)=x^-2

step 1 So in this problem we are asked to find f prime at a when half of x is X to the -2. Well, by def

Question

Find $f^{\prime}(a)$. $f(x)=x^{-2}$

   Find $f^{\prime}(a)$.
$f(x)=x^{-2}$

Calculus

James Stewart 7th Edition

Chapter 2, Problem 30

Instant Answer

Solved by Expert David Mccaslin

08/26/2021

Step 1

We are given the function $ f(x) = x^{-2} $ and need to find the derivative $ f^{\prime}(a) $. Show more…

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Find $f^{\prime}(a)$. $f(x)=x^{-2}$

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Key Concepts

Derivative

The derivative is a fundamental concept in calculus that quantifies the rate of change of a function with respect to its variable. It represents the slope of the tangent line to the function's graph at a given point, providing insight into the function's behavior locally.

Power Rule

The power rule is a basic differentiation technique used to compute the derivative of functions of the form f(x) = x^n. According to this rule, the derivative is found by multiplying by the exponent and reducing the exponent by one, resulting in f'(x) = n*x^(n-1).

Evaluation at a Point

Evaluating a derivative at a specific point involves substituting the value of the variable into the derivative function. This process gives the exact slope of the function at that point, which is essential for understanding the function's instantaneous rate of change.

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