# Explain the meaning of the given derivatives.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 3.4, Problem 76E

a.

To determine

## Explain the meaning of the given derivatives.

Expert Solution

### Explanation of Solution

Given:

The given derivatives are dvdr and dvdt .

Calculation:

dvdr its represent the rate of change of the volume per unit of the length of the radius.

dvdt its represent the rate of change of the volume per unit time.

b.

To determine

### Explain the relation between the given derivatives.

Expert Solution

The relation between given derivatives is dVdt=4πr2drdt .

### Explanation of Solution

Given:

The given derivatives are dvdr and dvdt .

Calculation:

dvdr its represent the rate of change of the volume per unit of the length of the radius.

dvdt its represent the rate of change of the volume per unit time.

Use formula of the volume of a sphere.

V=43πr3

Now,

dVdt=ddt(43πr3)dVdt=43πddt(r3)dVdt=43π3r2drdtdVdt=4πr2drdt

Hence the relation between given derivatives is dVdt=4πr2drdt .

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