   Chapter 11, Problem 23RE ### 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

# Suppose 3 x 2 − 2 y 3 = 10 y , where x and y are differentiable functions of t. If d x / d t = 2 , find d y / d t when x = 10 and y = 5.

To determine

To calculate: The value of dydt if 3x22y3=10y for x=10,y=5anddxdt=2.

Explanation

Given Information:

The provided equation is:

3x22y3=10y

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:

3x22y3=10y

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

ddt(3x2)ddt(2y3)=ddt(10y)

Now, use the chain rule to obtain the derivative:

ddt(3x2)ddt(2y3)=dd

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