/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 73 Find the derivative of: \(\mathr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 73

Find the derivative of: \(\mathrm{y}=\mathrm{x}^{3 \mathrm{~b}}\).

Short Answer

Expert verified
The derivative of \(y = x^{3b}\) with respect to x is \(y' = 3bx^{3b-1}\).

Step by step solution

01

Identify the function and the exponent

We have the function, \(y = x^{3b}\), where the exponent, n, is 3b in this case.
02

Apply the power rule for derivative

According to the power rule, the derivative of \(y = x^n\) with respect to x, \(y'\), is given by: \(y' = nx^{n-1}\). Here, n = 3b, which we substitute into the equation to find the derivative with respect to x: \(y' = (3b)x^{(3b-1)}\).
03

Simplify the answer

The final derivative of the given function is: \(y' = 3bx^{3b-1}\). So, the derivative of \(y = x^{3b}\) with respect to x is \(y' = 3bx^{3b-1}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find \(\mathrm{f}\) (x) from \(\mathrm{f}(\mathrm{x})=2^{5} \sqrt{\mathrm{x}} 3\).

Find the general expression for the \(\mathrm{n}^{\text {th }}\) derivative of: \(f(x)=[1 /(3 x+2)]\)

Find the derivative of: \(f(x)=\left[\left\\{(x-1)^{2} \sqrt{(2 x+3)\\}} /\left\\{(x+4)^{3}(2 x-1)^{4}\right\\}\right]\right.\)

Find \(D^{2} y\) and \(D^{3} y\), if \(y=\left[(x) /\left(1+x^{2}\right)\right]\).

If \(\mathrm{y}=\mathrm{u}^{2}\), and \(\mathrm{x}=(\mathrm{u}-1) /(\mathrm{u}+1)\), find \(\mathrm{dy} / \mathrm{d} \mathrm{x}\).
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.