Calculus Know-It-ALL by Stan Gibilisco

Author:Stan Gibilisco
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2009-12-30T16:00:00+00:00

Practice Exercises

This is an open-book quiz. You may (and should) refer to the text as you solve these problems. Don't hurry! You'll find worked-out answers in App. C. The solutions in the appendix may not represent the only way a problem can be figured out. If you think you can solve a particular problem in a quicker or better way than you see there, by all means try it!

1. Differentiate the inverse of the following function over the domain x > 0. First, find the inverse and then differentiate it directly. Then, use the "back door" method.

f(x) = x2 + 2

2. Differentiate the inverse of the following function over the domain x > 0. First, find the inverse and then differentiate it directly. Then, use the "back door" method.

f(x) = ln x

3. Differentiate the inverse of the following function. First, find the inverse and then differentiate it directly. Then, use the "back door" method.

f(x) = x5 + 4

4. Define the domain of the following function. Then, differentiate it with respect to x.

f(x) = 5 Arcsin x

5. Define the domain of the following function. Then, differentiate it with respect to t.

g(t) = −6t2 Arcsin t

6. Define the domain of the following function. Then, differentiate it with respect to z.

h(z) = Arccos z2

7. Define the domain of the following function. Then, differentiate it with respect to v.

f(v) = 3v3 Arccos (v/3)

8. Define the domain of the following function. Then, differentiate it with respect to s.

h(s) = Arcsin s3 − Arccos 2s

9. Define the domain of the following function. Then, differentiate it with respect to w.

g(w) = (Arccos w2 − Arcsin w2)/2

10. Define the domain of the following function. Then, differentiate it with respect to x.

f(x) = Arcsin ex

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