   Chapter 11.4, Problem 74E 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 67-74, find the indicated derivative. In each case the independent variable is a (unspecified) differentiable function of t. [HINT: See Quick Example 4.] y = x + 1 x , x = 9  when  t = 1 , d x d t | t = 1 = − 1  Find  d y d t | t = 1

To determine

To calculate: The derivative dydt|t=1 of the function y=x+1x.

Explanation

Given Information:

The provided function is y=x+1x.

Formula used:

Derivative of function f(x)=(u)n using chain rule is f'(x)=ddx(u)n=nun1dudx, where u is the function of x and dudx is unspecified.

Calculation:

Consider the function, y=x+1x

Convert the function in exponential form,

y=x1/2+x1/2

Apply the chain rule,

dydt|t=1=12x1/2dxdt12x3/2dxdt

Substitute dxdt|t=1=1 in dydt|t=1=12x1/2dxdt12x3/2dxdt as,

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