Implicit Differentiation: How to Differentiate Functions with Respect to x

[nokia8650]

If one was to differntiate a function implicity eg.

sin x + cos y = 5,

would one show this by writing:

d/dx(sin x + cos y = 5)

= and then differentiate with respect to x? I wasnt sure whether or not the bracket goes around the whole thing or just the left hand side.


Thanks

 

[tiny-tim]

If one was to differntiate a function implicity eg.

sin x + cos y = 5,

would one show this by writing:

d/dx(sin x + cos y = 5)

= and then differentiate with respect to x? I wasnt sure whether or not the bracket goes around the whole thing or just the left hand side.


Thanks

Hi nokia8650!

Definitely the whole thing!

Whatever you do to one side of an equation, you must do to the other.

That's what equality is all about! ​

 

[armis]

Hmm, I never thought about that. Now I'll know it's correct
However, I use this notation
\sin{x}+\cos{y}=5\mid\cdot{d/dx}
it's just seems more convenient
That's exactly the same thing isn't it?

I know it's a REALLY silly question but I just wanted to make sure

 

[tiny-tim]

\sin{x}+\cos{y}=5\mid\cdot{d/dx}

Hi armis!

(are you the same person as nokia8650?)

I don't really understand that.

Can you show how the next couple of lines would go, so that we can see it in actual use?

 

[armis]

Hi tiny-tim

Nop, I am not the same person :)

Sure
\sin{x}+\cos{y}=5\mid\cdot{d/dx}
We get
\cos{x}=0 if y is not a function of x

Most of our lecturers do that so I was wondering why bother writting ()

 

[tiny-tim]

Hi armis!

It looks weird to me …

but if your lecturers do it, I suppose it's ok.

I think writing the () is better because it avoids any possibility of ambiguity …

also, that vertical stroke may be clear on a whiteboard, where the lecturer can make it really large, but it's not so clear on paper or in a book.

 

[armis]

I find it weird you haven't seen it :) Well, maby I am the weird one and it may just be a matter of convenience for the lecturers as sometimes they have to write down REALLY a lot of stuff on the whiteboard
I am just so used to it that I could hardly think of writting () :)
But yeah, () avoids any possibility of ambiguity (phew... that was a hard one for me, I am not an english speaker)
Indeed the vertical stroke is larger than the one I showed as I couldn't find one large enough in the LaTeX