Find f^''(x). f(x)=1 / √(x)

Name: Problem 6, Chapter 3: Calculus with Concepts in Calculus
Uploaded: 2022-04-03T16:43:15-08:00
Duration: 2 min 1 s
Channel: Mirza Aslam Beig
Description: Find f^''(x). f(x)=1 / √(x)

step 1 Okay, the question is to find out the second derivative of the given function and we have the fu

Question

Find $f^{\prime \prime}(x)$. $$ f(x)=1 / \sqrt{x} $$

   Find $f^{\prime \prime}(x)$.
$$
f(x)=1 / \sqrt{x}
$$

Calculus with Concepts in Calculus

Denny Gulick, Robert… 6th Edition

Chapter 3, Problem 6

Instant Answer

Solved by Expert Mirza Aslam Beig

04/03/2022

Step 1

We can write $f(x) = 1 / \sqrt{x}$ as $f(x) = x^{-1/2}$. Show more…

Show all steps

Thanks for your feedback!

Find $f^{\prime \prime}(x)$. $$ f(x)=1 / \sqrt{x} $$

Play audio

Feedback

Mirza Aslam Beig and 70 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

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

Radical and Exponential Notation

This concept involves rewriting radical expressions as expressions with fractional exponents. For example, the square root of x is written as x^(1/2), and its reciprocal, 1/sqrt(x), becomes x^(-1/2). This transformation simplifies the process of differentiation using algebraic rules.

Power Rule for Differentiation

The power rule is a fundamental tool in calculus that allows us to differentiate functions of the form x^n. According to this rule, the derivative of x^n is n*x^(n-1). Applying this rule to functions expressed with fractional exponents enables straightforward computation of their derivatives.

Please give Ace some feedback