   Chapter 9, Problem 75RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

75.  Fond d y d x  if  y = [ ( 3 x + 1 ) ( 2 x 3 − 1 ) ] 12 .

To determine

To calculate: The simplified form of the derivative of y=[(3x+1)(2x31)]12.

Explanation

Given Information:

The function is y=[(3x+1)(2x31)]12.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the coefficient rule of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the sum rule of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

According to the product rule, if f(x)=u(x)v(x), then

f(x)=u(x)v(x)+v(x)u(x)

The derivative of a constant value, k, is

ddx(k)=0

According to the chain rule differentiation, if y=f(u), where u=g(x), then y is a differentiable function of x.

dydx=dydududx

Calculation:

Consider the provided function,

y=[(3x+1)(2x31)]12

Consider (3x+1)(2x31) to be u,

y=u12

Differentiate both sides with respect to x,

dydx=ddx(u12)

Simplify using the power rule, and use the chain rule to evaluate

dydx=12u121dudx=12u11dudx

Substitute (3x+1)(2x31) for u,

dydx=12((3x+1)(2x31))11ddx((3x+1)(2x31))

Simplify the internal derivative ddx((3x+1)(2x31)) using the product rule,

dydx=12((3x+1)(2x31))11((d

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

In Exercises 17-20, determine whether the point lies on the graph of the function. 20. (3,113);h(t)=|t+1|t3+1

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

Convert the expressions in Exercises 8596 radical form. x1/3y3/2

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the definite integral. 0axa2x2dx

Single Variable Calculus: Early Transcendentals

0 1 2 ∞

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