differentiate (1 Viewer)

[barbernatorr]

ALSO @TIMSKE YOU GOT PHYSICS TOMORROW. WHY ARE YOU ON?!

Does that mean that u also have physics tomorrow?

 

[SpiralFlex]

^No. I just like peeping into little bedrooms of little boys.

 

[deswa1]

^No. I just like peeping into little bedrooms of little boys.

Interesting phrasing...

 

[Timske]

^No. I just like peeping into little bedrooms of little boys.

i like that please do et moar

 

[SpiralFlex]

^k. Do you have contact with Miss Arlena? If so, PM.

 

[Timske]

^k. Do you have contact with Miss Arlena? If so, PM.

Yes but i'm not giving it to a robot

 

[Sanjeet]

Also for 4U students who can implicitly differentiate, this also comes in handy for a few types of questions:
<img src="http://latex.codecogs.com/gif.latex?y=a^x\\ lny=xlna\\ (\frac{1}{y})(\frac{dy}{dx})=lna\\ \frac{dy}{dx}=(y)lna\\ \frac{dy}{dx}=(a^x)lna" title="y=a^x\\ lny=xlna\\ (\frac{1}{y})(\frac{dy}{dx})=lna\\ \frac{dy}{dx}=(y)lna\\ \frac{dy}{dx}=(a^x)lna" />

How do you get from the 2nd to 3rd line?

 

[Aesytic]

How do you get from the 2nd to 3rd line?

differentiate both sides with respect to x, RHS is self-explanatory, with LHS, you use the chain rule --> (d/dy)*(dy/dx) = d/dx
.'.d/dx(lny) = d/dy(lny)*(dy/dx)
= (1/y)(dy/dx)

 

[Sanjeet]

Thanks, I just learnt implicit differentiation today, not sure why us 3U students aren't taught it though it comes in handy.

 

[Carrotsticks]

Thanks, I just learnt implicit differentiation today, not sure why us 3U students aren't taught it though it comes in handy.

Because in Extension 1 Mathematics, the only questions ever asked do not require Implicit Differentiation to sketch.

The only ones that really do require implicit differentiation are the ones that are non-linear in terms of the output Y.

For example, the standard polynomial like this:



... is linear in terms of Y because we just have plain Y, not Y^2 or anything. Suppose we have ay+b instead of y, we can easily re-arrange it such that Y becomes the subject.

However, something like this:



... is non-linear in terms of Y. So we require implicit differentiation.

 

[Sanjeet]

I see, but it does make some questions easier
e.g.

 

[deswa1]

I see, but it does make some questions easier
e.g.

Sorry, how does implicit make this question easier? You already have everything in terms of y so just use the product+chain rule...

 

[Sanjeet]

Sorry, how does implicit make this question easier? You already have everything in terms of y so just use the product+chain rule...

Multiply by

Multiplying by


Instead of finding the first and second derivative, and then plugging it in to make it work, which would take longer.

 

[deswa1]

That's nice. I like