/*! 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 17 Find the derivative of the funct... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 17

Find the derivative of the function. $$ y=4 t^{4 / 3} $$

Short Answer

Expert verified
The derivative of the function \(y = 4t^{4/3}\) is \(y' = (16/3)t^{1/3}\)

Step by step solution

01

Identify the function

In this case, the function to be derived is \(y = 4t^{4/3}\)
02

Apply the power rule

We want to apply the power rule of differentiation which states that if \(y = ax^n\), then the derivative \(y' = nax^{n-1}\). Thus, applying the power rule to our function we get, \(y'=(4/3)*4t^{4/3-1} = (16/3)t^{1/3}\).
03

Simplify the derivative

The derivative \(y' = (16/3)t^{1/3}\) is already simplified.

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

Use the General Power Rule to find the derivative of the function. $$ f(x)=\left(4 x-x^{2}\right)^{3} $$

Use the General Power Rule to find the derivative of the function. $$ h(x)=\left(4-x^{3}\right)^{-4 / 3} $$

Find an equation of the tangent line to the graph of \(f\) at the point \((2, f(2)) .\) Use a graphing utility to check your result by graphing the original function and the tangent line in the same viewing window. $$ f(x)=\left(4-3 x^{2}\right)^{-2 / 3} $$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ s(t)=\frac{1}{t^{2}+3 t-1} $$

Use the demand function to find the rate of change in the demand \(x\) for the given price \(p\). $$ x=300-p-\frac{2 p}{p+1}, p=\$ 3 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

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.