   Chapter 11.3, Problem 52E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 29-56, calculate d y d x . You need not expand your answers. [HINT: See Example 1 and 2.] y = ( 1 − 1 x 2 ) x 2 − 1

To determine

To calculate: The derivative of function y=(11x2)x21.

Explanation

Given Information:

The function is y=(11x2)x21.

Formula used:

Quotient rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f'(x)g(x)f(x)g'(x)[g(x)]2 where, g(x)0.

Derivative of function y=xn using power rule is dydx=nxn1.

Difference rule of derivative is ddx[f(x)g(x)]=ddx[f(x)]ddx[g(x)] where, f(x) and g(x) are any two differentiable functions.

Reverse identity of sum of squares is x2+2xy+y2=(x+y)2.

Calculation:

Consider the function, y=(11x2)x21.

Convert to power form,

y=1x2x21

Apply quotient rule of derivative,

dydx=ddx(1x2)(x21)(1x2)ddx(x21)(x21)2

Apply difference rule of derivative,

dydx=[ddx(1)ddx(x2)](x21)(1x2)[ddx(x2)ddx(1)](x21)2

Apply power rule and constant derivative rule,

dydx</

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 43-46, find f(a + h) f(a) for each function. Simplify yoiir answer. 43. f(x) = 3x + 4

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

For f(x) = 5 + g(x), f(x) = _____. a) 5g(x) b) 5 + g(x) c) 0 g(x) d) g(x)

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

True or False: converges.

Study Guide for Stewart's Multivariable Calculus, 8th 