   Chapter 11.3, Problem 46E 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 2 + 9 x − 1 x 2 + 2 x − 1

To determine

To calculate: The derivative of function y=x2+9x1x2+2x1.

Explanation

Given Information:

The function is y=x2+9x1x2+2x1.

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=x2+9x1x2+2x1.

Apply quotient rule of derivative,

dydx=ddx(x2+9x1)(x2+2x1)(x2+9x+1)ddx(x2+2x1)(x2+2x1)2

Apply sum and difference rule of derivative,

dydx=[ddx(x2)+ddx(9x)ddx(1)](x2+2x1)(x2+9x+1)[ddx(x2)+ddx(2x)ddx(1)](x2+2x1)2

Apply constant multiple rule of derivative,

dydx=[ddx(x2)+9ddx(x)ddx(1)]

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