   Chapter 11.3, Problem 41E 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 = ( x + 1 ) ( x + 1 x 2 )

To determine

To calculate: The derivative of function y=(x+1)(x+1x2).

Explanation

Given Information:

The function is y=(x+1)(x+1x2).

Formula used:

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)

Sum 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.

Derivative of a constant is 0.

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

Calculation:

Consider the function, y=(x+1)(x+1x2).

Convert to power form,

y=(x12+1)(x12+x2)

Apply product rule of derivative,

dydx=ddx(x12+1)(x12+x2)+(x12+1)ddx(x12+x2)

Apply sum rule of derivative,

dydx=[ddx(x12)+ddx(1)](x12+x2)+(x12

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