/*! 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 11 Find the derivative of the funct... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 11

Find the derivative of the function. $$ g(x)=x^{2}+5 x $$

Short Answer

Expert verified
The derivative of the function \( g(x) = x^2 + 5x \) is \( g'(x) = 2x + 5 \).

Step by step solution

01

Identify Functions and Constants

The function given is \( g(x) = x^{2} + 5x \). You can see that this is composed of two parts: \( x^2 \) (a function with power 2) and \( 5x \) (a constant 5 times a function).
02

Apply the Power Rule

Start with the function \( x^2 \). By applying the power rule, where \( (x^n)' = n\cdot x^{(n-1)} \), the derivative of the function \( x^2 \) is \( 2\cdot x^{(2-1)} \). So, the derivative of \( x^2 \) is \( 2x \).
03

Apply the Constant Rule

Next, apply the constant rule to the function \( 5x \). According to the constant rule, the derivative of a constant times a function is just the constant times the derivative of the function. Thus, the derivative of \( 5x \) will be \( 5 \cdot 1 \) since the derivative of \( x \) is \( 1 \). This gives you \( 5 \).
04

Combine the Results

Lastly, combine the derivatives from the previous steps. This gives \( 2x + 5 \) as the final result.

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

Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=(3 x+1)^{-1} $$

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. $$ f(x)=3(9 x-4)^{4} $$

Use a graphing utility to graph \(f\) and \(f^{\prime}\) on the interval \([-2,2]\). $$ f(x)=x(x+1)(x-1) $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

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.