Implicit and Explicit Differentiations? | Page 1 | Mathematics | Guild Forums

Dr. Leonard McCoy

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Posted: Mon Sep 25, 2006 12:43 pm

Okay, I understand the difference, but I am having trouble remembering which one is which... So is there an easy way to straighten it out in my pea-brain?

That and if someone has a good unit circle for trig functions (I have no idea how to explain it better), I would greatly appreciate it! mrgreen

Thanks in advance!

Posted: Mon Sep 25, 2006 8:14 pm

Look in the "Oh noes, its trig" thread for Layra's unit circle displaying ALL the trig functions; it's the coolest thing I've ever seen.

In single-variable calculus, implicit differentiation is required anytime you have both y and x in the same equation. In other words, if you have a certain equation in which you can't describe y in terms of x (get them on opposite sides of = ), you need to differentiate implicitly.

Swordmaster Dragon

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jestingrabbit

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Posted: Tue Sep 26, 2006 9:51 am

Swordmaster Dragon

In other words, if you have a certain equation in which you can't describe y in terms of x (get them on opposite sides of = ), you need to differentiate implicitly.

Not just get them on opposite sides of an equal sign, but be able to write y as a function of x. For instance:

y^8+7y+3 = e^x +x

is going to need implicit differentiation, whereas if you've got something like

y= f(x)

then you can do it explicitly. There isn't that much difference with the calculation required though.

Posted: Wed Sep 27, 2006 11:36 am

jestingrabbit

Swordmaster Dragon

In other words, if you have a certain equation in which you can't describe y in terms of x (get them on opposite sides of = ), you need to differentiate implicitly.

Not just get them on opposite sides of an equal sign, but be able to write y as a function of x. For instance:

y^8+7y+3 = e^x +x

is going to need implicit differentiation, whereas if you've got something like

y= f(x)

then you can do it explicitly. There isn't that much difference with the calculation required though.

Yay!!! symbols instead of a blur of words!!! Woot! Ok.. Now I just need to make a stupid jingle to keep them separate in my mind...

Dr. Leonard McCoy

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Swordmaster Dragon

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Posted: Thu Sep 28, 2006 12:39 pm

Gah! I can't believe I forgot about that...after a while, you kinda stop caring about the difference. Or rather, you don't realize that you're doing it instinctively.

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