   Chapter 11.3, Problem 68E 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 63-70, use the calculation thought experiment to say whether the expressing is written as a sum, difference, scalar multiple, product, or quotient. Then use the appropriate rules to find its derivative [HINT: See Quick Example 3-7 and Example 3.] y = ( x + 2 ) x x + 1 (Do not simplify the answer.)

To determine

To calculate: The derivative of the function y=(x+2)xx+1 and also explain the expression is either of them: Sum, Difference, Scalar multiple, product or quotient by use of the calculation through experiment.

Explanation

Given Information:

The provided function is y=(x+2)xx+1.

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.

Product 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)

A derivative of a constant is 0.

A derivative of a function y=xn using power rule is dydx=nxn1.

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

Calculation:

Consider the function y=(x+2)xx+1,

According to calculation through experiment, the expression of y is a quotient expression.

So, apply the quotient rule.

dydx=ddx[(x+2)x](x+1)(x+2)xddx(x+1)(x+1)2

Apply product rule and sum rule,

dydx=[ddx(x+2</

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