   Chapter 11.6, Problem 44E 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 43-52, use logarithmic differentiation to find d y / d x . Do not simplify the result. [HINT: See Example 4.] y = ( 3 x + 2 ) ( 8 x − 5 )

To determine

To calculate: The value of dydx for function y=(3x+2)(8x5) using the logarithmic differentiation.

Explanation

Given information:

The provided function is y=(3x+2)(8x5).

Formula used:

The derivative of natural logarithm of a function is ddxlnu=1ududx.

Constant multiple rule of derivative of function f(x) is f(cx)=cf(x) where c is constant.

Calculation:

Consider the provided function,

y=(3x+2)(8x5)

Now, take natural logarithm on both sides of the function as,

lny=ln[(3x+2)(8x5)]

Simplify the above expression as,

lny=ln(3x+2)+ln(8x5)

Then, take ddx of both sides on the above expression,

ddx(lny)=ddx(ln(3x+2)+ln(8x5))=ddx[ln(3x+2)]+ddx[ln(8x5)]

The derivative of natural logarithm of a function is ddxlnu=1ududx.

Apply the above formula for the derivative,

ddx(lny)=ddx[ln(3x+2)]+ddx[ln(8x5)]1ydydx=1(3x+2)ddx

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