   Chapter 11.4, Problem 73E 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 3 + 1 x , x = 2  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=x3+1x.

Explanation

Given Information:

The provided function is y=x3+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=x3+1x

Apply the chain rule,

dydt|t=1=3x2dxdt(1x2dxdt)=3x2dxdt1x2dxdt

Substitute dxdt|t=1=1 in dydt|t=1=3x2d

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