   Chapter 11.1, Problem 12E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find d s d q  if  s  = ln ( q 2 4 + 1 ) .

To determine

To calculate: The value of dsdq for the function s=ln(q24+1).

Explanation

Given Information:

The provided function is s=ln(q24+1).

Formula Used:

The quotient rule for any positive numbers M and N, lnMN=lnMlnN.

Derivative of natural logarithmic functions is such that, if y=lnu, where u is a differentiable function of x then dydx=1ududx.

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Calculation:

Consider the function, s=ln(q24+1)

Rearrange the function.

s=ln(q2+44)

Use quotient rule for logarithms,

s=ln(q2+4)ln4

Differentiate with respect to q

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