Question

what are the 1st partial derivatives of f(x) = 5yx+4y^2

Answer 1

\[f_x = 5y + 0\\f_y = 5x + 8y\]

When differentiating with respect to x, treat y as a constant and apply all normal diff. rules. Same when WRT y, but treat x as a constant.

Answer 2

\[f_x = \frac{\delta}{\delta x} \\ f_y = \frac{\delta}{\delta y}\]

Answer 3

I don't get it what is the d/dx is that like division?

Answer 4

Those are curly ds signifying partial differentiation.

Answer 5

similar to \[\frac{d}{dx}f(x) = f'(x)\]

It's just notation. Liebniz vs Newtonian

Answer 6

\[\frac{\delta}{\delta x}f(x) = f_x\] when partial wrt to x

Answer 7

but what is 2 + 9? and how can i divide the numerator by a piece of the matrices in 4-space?

Answer 8

....

Answer 9

2 + 9 is 11. Let's say your numerator is 20. You have a denominator of 5. \[\frac{20}{5} = 4\]

And the rest of your question makes no sense.

Answer 10

Okay wow that is real amazing

Answer 11

well if the partial fx is 5y then what is 2nd order partial wrt x?

Answer 12

zero

Answer 13

because there is no x in your expression, it is a constant

Answer 14

ok

Answer 15

what about 2nd order fxy

Answer 16

\[f_{xy} = 5\]

Answer 17

which by some theorem means \[f_{yx} = 5\]

Answer 18

mixed order 2nd order partials are equivalent

Answer 19

ok cool

Answer 20

ty

Answer 21

wait but what about fey

Answer 22

Do you mean \[f_{yy}\]

Answer 23

yes

Answer 24

8

Answer 25

OK but then what do i do if I can't figure out how to differentiate

Answer 26

what do you mean?

Answer 27

like if i have to use chain rule, i don'e like it

Answer 28

lol

Answer 29

how do i find expected value of continuous random variables

Answer 30

? what class

Answer 31

i don't know it just homework

Answer 32

what class?

Answer 33

probably theories?

Answer 34

you mean probability?

Answer 35

maybe, yes, yeah thats it

Answer 36

So you have a PDF, like, f(x) = some expressions for various values of x (typically ranges since the variable X is continuous)

Answer 37

so you find the limits of those ranges, and integrate each expression with respect to those limits, and sum your results after u anti-derive

Answer 38

(after u calculate the integrals)

Answer 39

that will be expected value (i.e., mean)

Answer 40

i forgot, you need to multiply each expression by x before integrating
that is

\[E(X) = \int_{-\infty}^{\infty} xf(x)dx \]

Answer 41

so like if f(x) = x^2 from 0 to 10 and 0, else, i integrate x*x^2 dx? so x^3 dx????

Answer 42

yeah you can ignore the 0 cuz it will integrate to zero, so just integrate from 0 to 10

\[\int_{0}^{10}x^3dx\] and that will be expected value

Answer 43

@Compassionate @shibainu @TheOcean @adrynicoleb