I have searched and different sources tell me different results:
considering y(x) is the function ,is the implitcit derivative of sin(y) = 0 or y'cos(y)???
my logic tells me to do the power rule and do the internal derivative (y') * external derivative (cos)
wolframalpha and other math calculators tell me its 0.
#Quick question about implicit derivatives
limpid hollow
pseudo oracleBOT
limpid hollow
also just to double check while im here
y(x) ' = dx/dy or y(x)'= dy/dx?
I always get it confused and the research made me even more confused
Tho i think its the latter
minor copper
Basically implicit differentiation relies on the chain rule
For your first question, you need to say what sin(y) is equal to, if there’s no other functions you could just say sin(y) = a constant
It’s the latter for your second question
The derivative of sin(y) is cos(y) dy/dx
Ie cos(y) y’
But if sin(y) = a constant, then dy/dx = 0 (because 0 divided by cos(y) is 0)
Assuming ofc that cos(y) isn’t 0
edgy pulsar
,w d/dx sin(y(x))
tawny idolBOT
edgy pulsar
i wonder if your wolfram was differentiating sin(y) = 0, like bottle said 
your thinking is right though
to be pedantic, y(x)' isn't a notation, it's y'(x) = dy/dx
if you need help remembering, you can pretend the apostrophe is a slash, then you get y/x which is like dy/dx 
just to remember which way around
limpid hollow
thank you guys!
whislt im here, im checking a completely different question about limits in which again
i have conflicinting answers
Would it be ok if i ask it here so i dont have to add another post ?
or should i just make another post anyway
limpid hollow
i wonder if your wolfram was differentiating sin(y) = 0, like bottle said <:eeve...
also here is what mine was saying
edgy pulsar
aha, you are taking the partial derivative of sin(y) with respect to x
limpid hollow
edgy pulsar
this is a different thing to the derivative, which will come up in calc III, but basically you are asking wolfram to treat sin(y) as a constant
kind of on them for calling this "implicit differentiation calculator"
but just make sure it says $\dv{x}$ and not $\frac{\partial}{\partial{x}}$
limpid hollow
yeah im not super used to using wolfram alpha so i dont really know honestly
I usually use other apps that are more common here
edgy pulsar
fair, im not a big wolfram alpha person either
limpid hollow
this is a different thing to the derivative, which will come up in calc III, but...
i actually have already done all the way to calc 4
finished it all up
but my girfrield just got into uni and she is taking calc 1
so im revisiting everything again
and as a good calc 1 student i remember almost nothing
tawny idolBOT
haseeb
edgy pulsar
sorry that was bothering me
limpid hollow
np
edgy pulsar
well, you know your partial derivatives then, so that's what happened :P
edgy pulsar
and as a good calc 1 student i remember almost nothing
this is very real
i think for your limits question you should make another post
edgy pulsar
yeah theres no hard rule but seems different enough of a q for me
limpid hollow
this is very real
calc 1 was such a nightmare....
its quite ironic that calc 4 was actually the easiet
edgy pulsar
lol that's definitely different to my experience 😅 i think i remembered the most out of calc 3
limpid hollow
calc 3 was my favorite but
calc 4 was easier
i liked sums and series and such
dont actually remember much from calc 4 but i got a 9.2 or smth in my final grade
just remember it being chill
hopefully i havent forgotten it qwbjhenqweqw
verbal stump
https://tutorial.math.lamar.edu/
a useful website i found
limpid hollow
how do i change the tags to solved again