/*! 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 15 Find the derivative of the funct... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 15

Find the derivative of the function. $$ s(t)=t^{3}-2 t+4 $$

Short Answer

Expert verified
The derivative of the function \( s(t) = t^3 - 2t + 4 \) is \( ds/dt = 3*t^2 -2 \).

Step by step solution

01

Identify the function

The given function to differentiate is \( s(t) = t^3 - 2t + 4 \)
02

Apply the power rule of differentiation for each term

The power rule states that the derivative of a function in the form of \( t^n \) is \( n*t^(n-1) \). So, taking derivative of each term, the derivative of \( t^3 \) is \( 3*t^2 \), derivative of \( -2t \) is \( -2 \), and the derivative of constant 4 is zero because the slope of a constant function is zero.
03

Write the Derivative

Join the derivatives of individual terms to get the derivative of the function. So, the derivative of \( s(t) \) is \( 3*t^2 -2 \).

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 \(d y / d u, d u / d x\), and \(d y / d x\). $$ y=u^{3}, u=3 x^{2}-2 $$

Find an equation of the tangent line to the graph of the function at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. $$ f(t)=\left(t^{2}-9\right) \sqrt{t+2} \quad(-1,-8) $$

Match the function with the rule that you would use to find the derivative most efficiently. (a) Simple Power Rule (b) Constant Rule (c) General Power Rule (d) Quotient Rule $$ f(x)=\frac{2}{1-x^{3}} $$

Use the General Power Rule to find the derivative of the function. $$ f(x)=-3 \sqrt[4]{2-9 x} $$

Use the General Power Rule to find the derivative of the function. $$ s(t)=\sqrt{2 t^{2}+5 t+2} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.