Chap 22 Review

\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \]

Exercise 1 Which of the derivative rules should you use to find \[\partial_t e^{t^2}\ ?\]

Exercise 2 Which of the derivative rules should you use to find \[\partial_t e^{x^2}\ ?\]

Exercise 3 Which of the derivative rules should you use to find \[\partial_t e^t \sin(t)\ ?\]

Exercise 4 Which of the derivative rules should you use to find \[\partial_t e^t \sin(x)\ ?\]

Exercise 5 Which of the derivative rules should you use to find \[\partial_t \ln(t)\ ?\]

Exercise 6 Which of the derivative rules should you use to find \[\partial_t\, t\, e^{-t}\ ?\]

Exercise 7 Which of the derivative rules should you use to find \[\partial_x\ 37 x^5\ ?\]

Exercise 8 Which of the derivative rules should you use to find \[\partial_x\ 19\ ?\]

Exercise 9 Which of the derivative rules should you use to find \[\partial_x\ 15 x^2 - 3 x + 7 \ln(x)\ ?\]

Exercise 10 What is \(\partial_x\ 15 x^2 - 3 x + 7 \ln(x)\)?

Exercise 11 What is \(\partial_t e^k + \ln(e^2) - t\)?

Exercise 12 What is \(\partial_{x} \ln(x)/x^2\)? (Hint: You can write the function in a simpler way.)

\(-2 x^{-1} \ln(x)\) \(-2 x^{-3} \ln(x)\) \(x^{-3} \left(1 - 2 \ln(x)\right)\) \(-2 x^{-3} \left(1/x - 1\right)\)

question id: drill-Deriv-rules-12

Exercise 13 Which of these is \(\partial_t \left(ln(6)+t^4-e^t\right)\)?

Exercise 14 Which of these is \(\partial_u(\frac{1}{u^6}-\pi^3+4u^3+e)\)?

\(-6u^{-7}-3\pi^2+4u^3\)

\(-6u^{-5}-3\pi^2+12u^2+\frac{1}{e}\)

\(-6u^{-7}+12u^2\)

\(-6u^{-5}+12u^2 +\frac{1}{e}\)

question id: drill-Deriv-rules-12b

Exercise 15 Which of these is \(\partial_v(\sqrt[4]{v^7}+e^7-4-\frac{3v^6}{v^2})=\)

\(\frac{7}{4}\frac{1}{v^4}+7e^6-\frac{18v^5}{2v}\)

\(\frac{7}{4}v^{\frac{3}{4}}-12v^3\)

\(\frac{4}{7}v^{\frac{-3}{7}}-\frac{18v^5}{2v}\)

\(\frac{7}{4}v^{\frac{3}{4}}+e^7-12v^3\)

question id: drill-Deriv-rules-12c

Exercise 16 What is \(\partial_{t} \left(4 \sin(2\pi t) - 5\right)\)?

\(4 \cos(2\pi t) - 5\) \(4 \pi \cos(2 \pi t)\) \(8 \pi \cos(2 \pi t)\) \(8 \cos(2 \pi t)\)

question id: drill-Deriv-rules-13

Exercise 17 What is \(\partial_{t} \left(7 + 8 t^2 + 3 t^4\right)\)?

\(16 t + 12 t^3\) \(8 t + 4 t^3\) \(16 t^2 + 9 t^3\) \(4 t + 12 t^2\)

question id: drill-Deriv-rules-14

Exercise 18 The derivative \(\partial_x \text{dnorm}(x) = - x\, \text{dnorm}(x)\). What is \[\partial_x \text{dnorm}\left(\frac{x^2}{4}\right)\ ?\]

\(- \frac{x^3}{8} \text{dnorm}\left(\frac{x^2}{4}\right)\)

\(-\frac{x}{2} \text{dnorm}\left(\frac{x^2}{4}\right)\)

\(-\frac{x}{8} \text{dnorm}\left(\frac{x^2}{4}\right)\)

\(-\frac{x^2}{2} \text{dnorm}\left(\frac{x^2}{4}\right)\)

question id: drill-Deriv-rules-15

Exercise 19 What is \(\partial_{t} \left(6 t - 3 t^2 + 2 t^4\right)\)?

\(6 - 6 t + 8 t^3\) \(6 - 3 t + 6 t^3\) \(-3 t + 6 t^3\) \(6 - 3 t + 8 t^2\)

question id: drill-Deriv-rules-16

Exercise 20 What is \(\partial_t \ln(t^2 + 1)\)?

\(\frac{2t}{t^2+1}\) \(1/{t^2 + 1}\) \(1/2t\) \(2 t \ln(t^2 + 1)\)

question id: drill-Deriv-rules-17

Exercise 21 For the function \[g(t) \equiv \sin\left(\frac{2 \pi}{P} (t - t_0)\right)\] is the interior function linear?

Yes No

question id: drill-M08-1

Exercise 22 For the function \[g(P) \equiv \sin\left(\frac{2 \pi}{P} (t - t_0)\right)\] is the interior function linear?

Yes No

question id: drill-M08-2

Exercise 23 For the function \[h(u) \equiv \ln(a^2 u - \sqrt{b})\] is the interior function linear?

Yes No

question id: drill-M08-3

Exercise 24 For the function \(f(w) \equiv e^{kw}\), is the interior function linear?

Yes No

question id: drill-M08-4

Exercise 25 Saying “the interior function is linear” is not an entirely complete statement. A full statement is “the interior function is linear in terms of the input \(x\)” or “in terms of the input \(u\)” or whatever name we choose to use for the input.
Is the expression \(V x + U\) linear in terms of \(U\)?

Yes No

question id: drill-M08-5

Exercise 26 Saying “the interior function is linear” is not an entirely complete statement. A full statement is “the interior function is linear in terms of the input \(x\)” or “in terms of the input \(u\)” or whatever name we choose to use for the input.
Is the expression \(V x^2 + U\) linear in terms of \(U\)?

Yes No

question id: drill-M08-6

Exercise 27 Saying “the interior function is linear” is not an entirely complete statement. A full statement is “the interior function is linear in terms of the input \(x\)” or “in terms of the input \(u\)” or whatever name we choose to use for the input.
Is the expression \(V x^2 + U\) linear in terms of \(X\)?

Yes No

question id: drill-M08-7

No answers yet collected