   Chapter 3.2, Problem 18E

Chapter
Section
Textbook Problem

Differentiate. h ( r ) = a e r b + e r

To determine

To find: The differentiation of the function h(r)=aerb+er.

Explanation

Derivative rule:

(1) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]f1(x)ddx[f2(x)][f2(x)]2

(2) Power Rule: ddx(xn)=nxn1

(3) Sum rule: ddx(f+g)=ddx(f)+ddx(g)

(4) Constant multiple rule: ddx(cf)=cddx(f)

(5) Natural exponential function: ddx(ex)=ex

Calculation:

The derivative of the function h(r)=aerb+er is h(r), which is obtained as follows,

h(r)=ddr(aerb+er)

Use the quotient rule (1) and simplify the terms,

h(r)=(b+er)ddr(aer)(aer)ddr(b+er)(

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Convert the expressions in Exercises 6584 to power form. x3

Finite Mathematics and Applied Calculus (MindTap Course List)

A sample with a mean of M = 8 has X = 56. How many scores are in the sample?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 3540, rationalize the numerator of each expression. 37. 133

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

2 1 0 does not exist

Study Guide for Stewart's Multivariable Calculus, 8th

What graph has f′(2) > 0 and f″(2) < 0?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 