Chapter 3: Q. 29 (page 299)

$Given that u = u (t), v = v (t), and w = w (t) are functions of t and that k is a constant, calculate the derivative of each function f (t) in Exercises 27 - 36 . Your answers may involve u, v, w, \frac{d u}{d t}, \frac{d v}{d t}, \frac{d w}{d t}, k, a n d / o r t . f (t) = t v + k v$

Short Answer

Expert verified

$\frac{d f}{d t} = v + t \frac{d v}{d t} + k \frac{d v}{d t}$

Step by step solution

Step 1. Given information

A function, $f (t) = t v + k v$

Step 2. Derivative of given function

Differentiating the given function, we get,

$\frac{d f}{d t} = v + t \frac{d v}{d t} + k \frac{d v}{d t}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$Given that u = u (t), v = v (t), and w = w (t) are functions of t and that k is a constant, calculate the derivative of each function f (t) in Exercises 27 - 36 . Your answers may involve u, v, w, \frac{d u}{d t}, \frac{d v}{d t}, \frac{d w}{d t}, k, a n d / o r t . f (t) = t v + k v$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Derivative of given function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Giventhatu=u(t),v=v(t),andw=w(t)arefunctionsoftandthatkisaconstant,calculatethederivativeofeachfunctionf(t)inExercises27–36.Youranswersmayinvolveu,v,w,dudt,dvdt,dwdt,k,and/ort.f(t)=tv+kv

Short Answer

Step by step solution

Step 1. Given information

Step 2. Derivative of given function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Applied Mathematics

Logic and Functions

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

$Given that u = u (t), v = v (t), and w = w (t) are functions of t and that k is a constant, calculate the derivative of each function f (t) in Exercises 27 - 36 . Your answers may involve u, v, w, \frac{d u}{d t}, \frac{d v}{d t}, \frac{d w}{d t}, k, a n d / o r t . f (t) = t v + k v$