   Chapter 11.3, Problem 51E 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 x + 1 x 2 ) x + x 2

To determine

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

Explanation

Given Information:

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

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.

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.

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

Calculation:

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

Convert to power form,

y=x1+x2x+x2

Apply quotient rule of derivative,

dydx=ddx(x1+x2)(x+x2)(x1+x2)ddx(x+x2)(x+x2)2

Apply sum rule of derivative,

dydx=[ddx(x1)+ddx(x2)](x+x2)(x1+x2)[ddx(x)+ddx(x2)](x+x2)2

Apply power rule,

dydx=[1x11+(2)x21](x+x2)(x1+x2)[1x11+2x21](x+x2)2=(x22x3)(

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