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Chapter 3: Q. 29 (page 299)

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

Short Answer

Expert verified

dfdt=v+tdvdt+kdvdt

Step by step solution

01

Step 1. Given information

A function,f(t)=tv+kv

02

Step 2. Derivative of given function

Differentiating the given function, we get,

dfdt=v+tdvdt+kdvdt

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Most popular questions from this chapter

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=x2-xx2-3x+2

For each graph of f in Exercises 49鈥�52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical point. fx=x3+x2+1

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points .

fx=In2xx

For each graph of f in Exercises 49鈥�52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.
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