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You already have all the tools you need for differentiation. Do you have a specific example?

oh lol :)

lol

\[e^{2x}\div e^{4x ^{2}} + \cos(e ^{7x})\]

it approaches infinity?

i think i answered wrong lol

What do we need to do with the big messy problem? Take it's derivative?

And differentiate it

taking the derivative and differentiating are the same thing right?

Yes, just fancy words ^^

ok that's what i thought lol

Ok ok big question time c:

ok that makes sense = ) ty! and yes now to the big one lol

handy*

hold on lol cos is in the denominator with e to the 4x^2

Oh i see ^^

\[\large \left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v^2}\]

right that's what they did with it = ) that's where I got confused, not with the actual rule but u'

and v'

Remember how to do the chain rule? c:

yes

\[\huge \left(e^{2x}\right)'=e^{2x}(2)\]Any confusion on that one? c:

oh wow i think i just had a mental click lmfao

lol XD those are always fun.

hold on let me look at the problem and answer one more time lol

oh and then one more after that lol but i think it may be pretty easy haha

Since the base is LARGER than 1, and our exponent is positive, the value will explode.

What if you had,\[\large \lim_{x \rightarrow \infty} (.999)^x\]

so really big x values = really big y values

yah c:
As x approaches infinity, y is approaching infinity. In that first case.

I used a calculator but the bigger x gets the closer y goes to 0 for the second part

Yesss good good c:

correct = )

so in that case it would go to -infinity

Noooo :D An exponential can't go in the negative! :O

or wait it would go to 0 not -infinity right bc yeah what you just said haha

Ok simmer down :O Let's look at the first one a sec.

lol

yes

\[\large 4=a^2 \qquad \rightarrow \qquad a=2\]

ok that makes sense = ) is that a property or a rule?

It's this really fancy thing called "division" :3

lolol

or what i mean to say is how did you know to divide the points' equations hahahaha

We could have also done substition to get the same result though :)

like solve for C in one of the problems and then plug it into the other equation?

Yah :)

ok good i think i got it = ) thank you so much for all your help! = D

yay team \c:/

lol