Chap 25 Review

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

Exercise 6 What is $\partial_x A e^{kt}$?

$0$ $A k e^{kx}$ $t$

question id: PD06

Exercise 7 What is $\partial_t A e^{kt}$?

Exercise 8 What is $\partial_x A x e^{kt}$?

Exercise 9 What is $\partial_t A x e^{kt}$?

Exercise 10 What is $\partial_x \left[\strut a_0 + a_1 x + a_2 x^2 \right]$?

Exercise 11 What is $\partial_y \left[\strut a_0 + a_1 x + a_2 x^2 \right]$?

Exercise 12 What is $\partial_x \left[\strut a_0 + a_1 y + a_2 y^2 \right]$?

Exercise 13 What is $\partial_x \left[\strut a_0 + a_1 x + b_1 y + c x y \right]$?

Exercise 14 What is $\partial_y \left[\strut a_0 + a_1 x + b_1 y + c x y \right]$?

Exercise 15 What is $\partial_x \partial_y \left[\strut a_0 + a_1 x + b_1 y + c x y \right]$? (Usually we would write $\partial_{xy}$ instead of $\partial_x \partial_y$, but they amount to the same thing.)

Exercise 16 What is $\partial_x \partial_x \left[\strut a_0 + a_1 x + b_1 y + c x y \right]$? (Usually we would write $\partial_{xx}$ instead of $\partial_x \partial_x$, but they amount to the same thing.)

Exercise 17 What is $\partial_x \partial_x \left[\strut a_0 + a_1 x + b_1 y + c x y + a_2 x^2 + b_2 y^2 \right]$? (Usually we would write $\partial_{xx}$ instead of $\partial_x \partial_x$, but they amount to the same thing.)

Exercise 18 What is $\partial_y \partial_x \left[\strut a_0 + a_1 x + b_1 y + c x y + a_2 x^2 + b_2 y^2 \right]$? (Usually we would write $\partial_{yx}$ instead of $\partial_y \partial_x$, but they amount to the same thing.)

Exercise 19 What is $\partial_x \left[\strut A x^n y^m \right]$?

Exercise 20 What is $\partial_y \left[\strut A x^n y^m \right]$?

$A n x^{n-1} y^m$ $A n m x^{n-1} y^{m-1}$ $A m x^{n} y^{m-1}$ $A m y^{m-1}$

question id: PD20

Exercise 21 What is $\partial_{xy} \left[\strut A x^n y^m \right]$?

$A n x^{n-1} y^{m-1}$ $A n m x^{n-1} y^{m-1}$
$A m x^{n} y^{m-1}$ $A m x^{n-1} y^{m-1}$

question id: PD21

Exercise 22 What is $\partial_x \left[\strut f(x) + y\right]$?

Exercise 23 What is $\partial_x \left[\strut f(x) + g(y)\right]$?

$\partial_x f(x)$ $\partial_x f(x) + \partial_x g(y)$ $\partial_x f(x) + \partial_y g(y)$ $0$

question id: PD23

Exercise 24 What is $\partial_y \left[\strut f(x) + g(y)\right]$?

Exercise 25 What is $\partial_x \partial_y \left[\strut f(x) + g(y)\right]$?

Exercise 26 What is $\partial_y \partial_y \left[\strut f(x) + g(y)\right]$?

Exercise 27 What is $\partial_y f(x) g(y)$?

$\partial_y g(y)$ $f(x)\ \partial_{y} g(y)$ 0 $g(y)\ \partial_y f(x) + f(x) \ \partial_y g(y)$

question id: PD27

Exercise 28 What is $\partial_y h(x,y) g(y)$?

$\partial_y g(y)$ $g(y) \partial_y h(x, y)$ 0 $ g(y) _y h(x,y) + h(x,y) _y g(y)$

question id: PD28

Exercise 29 What is $\partial_x h(x,y) g(y)$?

$\partial_x h(x, y)$ $g(y)\ \partial_x h(x,y) + h(x,y)\ \partial_x g(y)$ $g(y) \partial_x h(x, y)$ $g(y) \partial_y h(x, y)$

question id: PD29

Exercise 30 What is $\partial_{yx} h(x,y) g(y)$?

$\partial_{yx} h(x, y)$

$g(y) \partial_{yx} h(x,y) + h(x,y)\ \partial_y g(y)$

$(\partial_y g(y)) \ (\partial_x h(x, y)) + g(y)\ (\partial_{yx} h(x, y))$

$(\partial_x g(y))\ (\partial_x h(x, y)) + g(y) (\partial_{xx} h(x, y) )$

question id: PD30

Exercise 31 What is the “with-respect-to” input in $\partial_y xy$?

$x$ $y$ $1$

question id: PD31

Exercise 32 What is the “with-respect-to” input in $\partial_x y$?

$x$ $y$ $1$

question id: PD32

Exercise 33 What is the “with-respect-to” input in $\partial_t y$?

$t$ $y$ $1$

question id: PD33

Exercise 34
You have been hiking all day and have reached map coordinate (x=2, y=2). You are completely exhausted. Time for a break. You want to walk along the hill, without any change of elevation. Which compass direction should you head in to get started?

No answers yet collected