[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vip /vp / vr / w / wg / wsg / wsr / x / y ] [Search | Home]
4Archive logo
from the chain rule we have
If images are not shown try to refresh the page. If you like this website, please disable any AdBlock software!

You are currently reading a thread in /sci/ - Science & Math

Thread replies: 22
Thread images: 7
File: xtvpX8B.jpg (187 KB, 1920x800) Image search: [iqdb] [SauceNao] [Google]
xtvpX8B.jpg
187 KB, 1920x800
from the chain rule we have
[math]
h(x) = f(g(x))
h(x)' = f(g(x))'g(x)'

\frac{\partial h(x))}{\partial x}=\frac{\partial f(g(x))}{\partial g(x)}\frac{\partial g(x)}{\partial x}
[/math]

but is the "expanded form" like so, for semantic understanding only of course.
>>
>>7803609
[math]
h(x) = f(g(x))
\newline
h(x)' = f(g(x))'g(x)'
\newline
\frac{\partial h(x))}{\partial x}=\frac{\partial f(g(x))}{\partial g(x)}\frac{\partial g(x)}{\partial x}
[/math]
>>
>>7803609
[math]h(x) = f(g(x)) \newline h(x)' = f(g(x))'g(x)' \newline [/math]

HOLY FUCK
[math]
\frac{\partial h(x))}{\partial x}=\frac{\partial f(g(x))}{\partial g(x)}\frac{\partial g(x)}{\partial x}[/math]
>>
>>7803614
please
[math]
h(x) = f(g(x))[/math]
[math] h(x)' = f(g(x))'g(x)'
[/math][math] \frac{\partial h(x))}{\partial x}=\frac{\partial f(g(x))}{\partial g(x)}\frac{\partial g(x)}{\partial x}[/math]
>>
[math]
h(x) = f(g(x))
[/math]
[math]
h(x)' = f(g(x))'g(x)'
[/math]
[math]
\frac{\partial h(x))}{\partial x}=\frac{\partial f(g(x))}{\partial g(x)}\frac{\partial g(x)}{\partial x}
[/math]
>>
>>7803616
the last one should be [math]\frac{\partial h}{\partial x} (x) = \frac{\partial f}{\partial x} (g(x)) \frac{\partial g}{\partial x} (x)[/math]

you have to differentiate first, and take the derivative at the appropriate point
>>
What is your point?
>>
File: CodeCogsEqn (1).png (3 KB, 214x144) Image search: [iqdb] [SauceNao] [Google]
CodeCogsEqn (1).png
3 KB, 214x144
>>7803625
so number 2 is correct?
>>
>>7803629
yes

f'(g(x)) means "the derivative of f taken at the point g(x)".

derivative of f is df/dx
derivative of f taken at the point g(x) is the function df/dx evaluated at the point g(x).
>>
File: CodeCogsEqn (1).gif (751 B, 95x42) Image search: [iqdb] [SauceNao] [Google]
CodeCogsEqn (1).gif
751 B, 95x42
>>7803632
is this also correct then? if so how come g is at the bottom this time
>>
These are not partial derivatives and you should not be using that notation, since it leads to confusion.
>>
File: 1437481064022.jpg (44 KB, 561x265) Image search: [iqdb] [SauceNao] [Google]
1437481064022.jpg
44 KB, 561x265
>>7803642
can you please explain or atleast link me, Im really lost :c

>pic related, my solid foundation in calculus
>>
>>7803645
all he means is that when you're referring to a derivative of a single variable function you just use a d

you're using the symbol for partial differentiation, as though f and g are multivariable functions
>>
File: ashamed.gif (465 KB, 300x272) Image search: [iqdb] [SauceNao] [Google]
ashamed.gif
465 KB, 300x272
>>7803640
plz halp with this
>>
>>7803645
Well I'm sure you can find a derivation of the chain rule in many many places.
Partial differentiation implies that the function you are differentiating is implicitly dependent on the variable. I don't honestly know if it's the same in all cases and I don't plan to figure that out, but it can lead to confusion when interpreting the process, which I think is why you made this thread.
>>
>>7803640
that's when f is a function of g.

For example

f(t) = t^2 (f is a function of time).
but it turns out t= x/3 (t is a function of position).

But you can't just write df/dx easily, since f is not a function of x.
you can write df/dt * dt/dx


I think I see why you are confused.
you should really use f' to denote the derivative of a function of 1 variable.
There is no ambiguity. if f is the square function, f'(x) = 2x, f'(3t) = 2*(3t).

if you want to introduce a new variable, you need the chain rule.
>>
File: 1434957231029.jpg (213 KB, 782x1168) Image search: [iqdb] [SauceNao] [Google]
1434957231029.jpg
213 KB, 782x1168
>>7803669
I cant differentiate on how those two are different,

cant I view it like this
f(g)
h(x) = f(x^2)
so then g is a function of x

idun understand anything anymore :C
>>
>>7803640
if you were to use that notation, I think it's necessary to include a second term:
[math]
\partial_g f \cdot \partial_x g + \partial_x f
[/math]
>>
File: Untitled.png (52 KB, 730x812) Image search: [iqdb] [SauceNao] [Google]
Untitled.png
52 KB, 730x812
>>
>>7803691
you're right, just please stop using partial derivatives. For the love of all that is the false god.
>>
>>7803697
>>7803625

so how come he wants me to do this crazy shit
>>
>>7803700
because he's an idiot. just do some example problems both ways and figure that shit out.
Thread replies: 22
Thread images: 7
Thread DB ID: 455968



[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vip /vp / vr / w / wg / wsg / wsr / x / y] [Search | Home]

[Boards: 3 / a / aco / adv / an / asp / b / biz / c / cgl / ck / cm / co / d / diy / e / fa / fit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mu / n / news / o / out / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / t / tg / toy / trash / trv / tv / u / v / vg / vip /vp / vr / w / wg / wsg / wsr / x / y] [Search | Home]

All trademarks and copyrights on this page are owned by their respective parties. Images uploaded are the responsibility of the Poster. Comments are owned by the Poster.
This is a 4chan archive - all of the shown content originated from that site. This means that 4Archive shows their content, archived. If you need information for a Poster - contact them.
If a post contains personal/copyrighted/illegal content, then use the post's [Report] link! If a post is not removed within 24h contact me at [email protected] with the post's information.