Posts Tagged ‘implicit’

I Are Okay at Implicit Differentiation (Now)

Friday, March 14th, 2008

Last week I got stuck working on basic differentiation - it was the implicit differentiation that threw me. This sentence in particular:

“In these cases [when an equation can't be transposed to make y the subject and you are finding the derivative of y with respect to x], y needs to be solved as a function of x”

Now I get it. You have to treat y as if it were x, but a little bit differently. So if:
y = 2y + 5

Instead of saying:
dy/dx = 2 (wrong)

You need to do this:
dy/dx =  2y’

So that problem I couldn’t solve last week - I totally solved it. I smashed the shit out of it. I can’t be bothered getting it and scanning it though, so if you don’t believe me go to hell.

So I said to the guy, “Hey, that’s my daughter!”
Group laughs

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I Are Suck at Implicit Differentiation!

Saturday, March 8th, 2008

As far as I understand, Implicit Differentiation is useful when y’ can’t directly be solved with respect to x, like in this equation:

x² - y³ = 8

The first way to try and get around this is to to transpose the equation, making y the subject, ie:

y = cuberoot(x² - 8 )

At this point, you can solve y’ with respect to x as per usual.

Sometimes, though, you can’t make solve for y.

“In these cases, y needs to be solved as a function of x” - I don’t completely get this - I’m going to ask about it though… Here’s where I get stuck:

Where I get stuck with implicit differentiation…

The answer’s supposed to be 4y!!!

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