   Chapter 4.5, Problem 64E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Chemistry The temperatures T ( in °F ) at which water boils at selected pressures p (in pounds per square inch) can be modeled by T   = 87.97   +   34.96  ln  p   +   7.91. Find the rate of change of the temperature when the pressure is 60 pounds per square inch.

To determine

To calculate: The rate of change of the temperature when the pressure is 60 pounds per square inch and the selected pressure p(in pounds per square inch) at the temperature T is approximated by T=87.97+34.96lnp+7.91p.

Explanation

Given information:

The provided function is T=87.97+34.96lnp+7.91p.

Formula used:

The derivative of function f(x)=un using the chain rule is,

f(x)=ddx(un)=nun1dudx

where u is the function of x.

Let u be a differentiable function of x is ddx[lnx]=1x,x>0 and ddx(lnu)=1ududx,u>0.

Calculation:

Consider the function,

T=87.97+34.96lnp+7.91p

The first order derivative of function T=87.97+34.96lnp+7.91p is,

Apply the logarithmic rule of derivative in function (lnp) and chain rule of derivative in function (7.91p),

dTdp=ddp(87

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