   Chapter 11.4, Problem 1E ### 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

# In Problems 1-4, find d y / d t using the given values. y = x 3 − 3 x  for  x  = 2,  d x / d t  = 4

To determine

To calculate: The value of dydt if y=x33x for x=2anddxdt=4.

Explanation

Given Information:

The provided equation is:

y=x33x

Formula used:

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x and:

dydx=dydududx

Calculation:

Consider the provided equation:

y=x33x

Now, differentiate both sides with respect to t to get:

ddt(y)=ddt(x3)ddt(3x)

Now, use the chain rule:

dydx=dydududx

To obtain the derivative of x3 as:

<

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