   Chapter 11.3, Problem 47E 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 0.23 − 5.7 x 1 − x − 2.9

To determine

To calculate: The derivative of function y=x0.235.7x1x2.9.

Explanation

Given Information:

The function is y=x0.235.7x1x2.9.

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.

Derivative of a constant is 0.

Constant multiple rule of derivative of function f(x) is ddx[cf(x)]=cddx[f(x)] where, c is constant.

Sum and 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.

Calculation:

Consider the function, y=x0.235.7x1x2.9.

Apply quotient rule of derivative,

dydx=ddx(x0.235.7x)(1x2.9)(x0.235.7x)ddx(1x2.9)(1x2.9)2

Apply difference rule of derivative,

dydx=[ddx(x0.23)ddx(5.7x)](1x2.9)(x0.235.7x)[ddx(1)ddx(x2

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