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[urban prism]

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[robust geyser]

@tidal frigate

[tidal frigate]

Hallo

[robust geyser]

So what is the outer function

It's x^1/2 right?

[tidal frigate]

Well

Outer function would be f(u)=e^u

Inner function would be g(x)=√x

Such that f(g(x))=e^√x

So to evaluate the derivative of f(g(x))

[robust geyser]

u?

Oh

So e^x is the outer one

[tidal frigate]

That'd just be this

So the derivative of e^u with respect to u is e^u

[robust geyser]

So it's e^x * 1/2x^-1/2

[tidal frigate]

Well still no

Can you just like

Hol on

The derivative of √x with respect to x is 1/2x^-1/2

[robust geyser]

alr

[tidal frigate]

Which we can simplify to 1/(2√x)

So our derivative is just (1/(2√x))•(e^u)

Then since u=√x

[robust geyser]

Yea I got that wooo

[tidal frigate]

Our derivative is (e^√x)/(2√x)

$\frac{e^{\sqrt{x}}}{2\sqrt{x}}$

[abstract vale]

Muus

[tidal frigate]

@robust geyser

[robust geyser]

Oh wait

[tidal frigate]

Do you get it now

[robust geyser]

So it stays as e^√x because of the rule that the e thing stays the same even when deriving it?

[tidal frigate]

In a sense yea

[robust geyser]

Is this quotient rule

@tidal frigate

[tidal frigate]

Yea

I mean you can use the quotient rule

[robust geyser]

but there's also chain rule on the top ffs bruh

[tidal frigate]

Yea but that's normal

[robust geyser]

So f'(x) would be a chain rule

the rest is normal

[tidal frigate]

Mhm

[robust geyser]

So the outer function I assume is e^-x since it stays the same

and then it's just -3

[tidal frigate]

No

Outer function e^u

Inner function -x^3

[robust geyser]

So -3x^-4

[tidal frigate]

Well no

[robust geyser]

For the inner one I meant

[tidal frigate]

But I think u were just careless

Try again

I know

[robust geyser]

-3x^2

[tidal frigate]

Yea

[robust geyser]

There

I'm actually slow asf

I got this

mb meant this

[tidal frigate]

Hold on

Try again

The derivative of x is 1

Not 1/x

Actually nvm a few mistakes

I'll just do part of it for you

[tidal frigate]

No

I mean I think there's a misconception on chain rule here

Sorry quotient rule I mean

So this is quotient rule

@robust geyser

[tidal frigate]

Here you multiplied by the whole fraction

When you should've just multiplied by the numerator

[robust geyser]

is it because the x and x^2 cancel out

[tidal frigate]

Here e^x should be e^(-x^3)

[tidal frigate]

No because that's the formula for quotient rule

[tidal frigate]

As seen here

@robust geyser

[robust geyser]

Wait wait I get it I think

@tidal frigate This should be correct

Also yea e^-x^3 is what's put on top I now understand why

[peak crystal]

Yeah, that’s good.

[gaunt quiver]

@robust geyser

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