10 Questions
| Total Attempts: 102

Questions and Answers

- 1.What does the equation (d/dx) .(c^ax)= c^ax (lnc .a), c>0 mean?
- A.
That the equation above is true for all c, but the derivative for c=0 yields a complex number

- B.
That the equation above is true for all c, but the derivative for c>0 yields a complex number

- C.
That the equation above is true for all c, but the derivative for c

- D.
That the equation above is true for all c, but the derivative for c yields a complex number.

- 2.What is the ideal number sentence describing logarithmic derivative?
- A.
Lnf= f/f

- B.
(lnf)'=f'/f

- C.
Lnf'=f/f'

- D.
Lnf'=f/1

- 3.What are the 2 arguments that define an inverse tangent?
- A.
F'(x,y)

- B.
(y,x)

- C.
Arctan (y,x).

- D.
F(x)'

- 4.What is the number sentence for the digamma function?
- A.
ψ0(x)

- B.
0(x)

- C.
ψ(x)

- D.
ψ0(x) +1

- 5.What is the set of rules that can help compute the derivative function?
- A.
Fa di Bruno's theorem and the general Leibniz rule.

- B.
Faa di Bruno's formula and the general Leibniz rule.

- C.
Faa di Bruno's theorem and the general Leibniz theorem.

- D.
The Bruno's theorem and the Leibnis rule.

- 6.What are the central objects of study in a complex analysis?
- A.
The polymorphic function

- B.
The holomorphic function

- C.
The morphological rule

- D.
The isomorphic rule

- 7.What is the Schwarzian derivative?
- A.
It is one that describes how a function is approximated by a fractional-linear map.

- B.
It is one that describes how a complex function is approximated by a fractional-linear map.

- C.
It is one that describes how a simple function is approximated by a fractional-linear map.

- D.
It is one that describes how a compounded function is approximated by a fractional-linear map.

- 8.Define the Wirtinger derivative? (pick the right answer.)
- A.
It's a set of differential operators permitting the construction of a differential calculus for complex functions.

- B.
It is one that completes a complex function is approximated by a fractional-linear map.

- C.
It is one that describes how a simple function is approximated by a fractional-linear map.

- D.
It is one that describes how a ordinary function is approximated by a fractional-linear map.

- 9.What is the role of the functional derivative?
- A.
It is one with respect to a function of a functional on a space of formulas.

- B.
It is one with respect to a function of a functional on a space of functions.

- C.
It is one with respect to a function of a functional on a space of rules.

- D.
It is one with respect to a function of a functional on a space of domains.

- 10.Explain the Frechet derivative?
- A.
It allows the extension of the directions derivatives to a general Banach space.

- B.
It allows the restrictions of the directions derivatives to a general Banach space.

- C.
It allows the construction of the directions derivatives to a general Banach space.

- D.
It shrinks the extension of the directions derivatives to a general Banach space.