Chapter 3: Q. 27 (page 299)

$Given that u = u (t), v = v (t), and w = w (t) are functions of t and that k is a constant, calculate the derivative of each function f (t) in Exercises 27 - 36 . Your answers may involve u, v, w, \frac{d u}{d t}, \frac{d v}{d t}, \frac{d w}{d t}, k, a n d / o r t . f (t) = u^{2} + k v$

Short Answer

Expert verified

$\frac{d f}{d t} = 2 u \frac{d u}{d t} + k \frac{d v}{d t}$

Step by step solution

Step 1. Given information

A function, $f (t) = u^{2} + k v$

Step 2. Derivative of given function

Differentiating the given function, we get,

$\frac{d f}{d t} = 2 u \frac{d u}{d t} + k \frac{d v}{d t}$

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$Given that u = u (t), v = v (t), and w = w (t) are functions of t and that k is a constant, calculate the derivative of each function f (t) in Exercises 27 - 36 . Your answers may involve u, v, w, \frac{d u}{d t}, \frac{d v}{d t}, \frac{d w}{d t}, k, a n d / o r t . f (t) = u^{2} + k v$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Derivative of given function

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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)=u2+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

Discrete Mathematics

Decision Maths

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Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

$Given that u = u (t), v = v (t), and w = w (t) are functions of t and that k is a constant, calculate the derivative of each function f (t) in Exercises 27 - 36 . Your answers may involve u, v, w, \frac{d u}{d t}, \frac{d v}{d t}, \frac{d w}{d t}, k, a n d / o r t . f (t) = u^{2} + k v$