calculus

[thorn cave]

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[slow sierra]

Can someone please show me how to simplify what I have to the stuff in the red

[peak orbit]

Hmm...

You want us to simplify the expression with the help of the red text?

[slow sierra]

Yep

So what I got is in the black

And the textbook answer is in the red

[hollow mesa]

...you just separate the fractions.

[slow sierra]

Thank youu

Idk how I missed that

[peak orbit]

I just equated both of the terms, the black and red text are both the same.

So it's just a matter of separating the fractions and simplifying.

[hollow mesa]

...I mean, obviously they're the same, or else one wouldn't simplify to the other.

[slow sierra]

I’m so confused

To like

When I should simplify

[peak orbit]

I have seen many cases where people ask to simplify it but both their answer and the real answers don't equalize.

[peak orbit]

Wdym?

[hollow mesa]

It doesn't super matter.

Like, all forms of an expression are necessarily equivalent, so you can just use whichever form is the most convenient for the application you have.

[slow sierra]

Yep I see

Thanks

[hollow mesa]

That's usually the most simplified form just because it's, y'know, simplified.

Like, if you ever want to actually do anything with the expression, the less simplified it is the more of a headache it'll be.

Outside of very specific contexts where you want it in a certain specific form because you, like, plan to transform it in some way based on that form.

[slow sierra]

Yep

[slow sierra]

Thanks

[zealous parrot]

@slow sierra has given 1 rep to @hollow mesa

[slow sierra]

Btw

Sorry to ask again

But

Do you have any idea how I can approach the second one? 😅

[hollow mesa]

Tangent is sine over cosine.

[slow sierra]

I tried that

I feel like I’m going in circles

[hollow mesa]

I meant all the way at the beginning.

tan(x)/cos(x) = (sin(x)/cos(x))/cos(x) = sin(x)/cos^2(x).

[slow sierra]

How did you know to do that

Like is what I did wrong?

[hollow mesa]

It's always easier to work with sine and cosine any time you have trig functions.

In any case, I'm not sure what form you're aiming for.

[marsh hatch]

hey do u guys know how to solve differentiation of ln(a^x)

[hollow mesa]

Go away.

[marsh hatch]

sorrryyy

[hollow mesa]

I don't want you to be sorry, I want you to be gone.

[marsh hatch]

ouch

[hollow mesa]

You didn't do anything "wrong", so far as I can tell.

Like, you're just asking how to simplify, but I don't know what you're simplifying towards.

[slow sierra]

Oh yep

Tbh I don’t really know either

I’m just trying to match my answer to the one given but I don’t know what they want which is why I’m confused

[hollow mesa]

What is the given answer?

Oh wait, is it still the thing in red? I didn't recognize it because it's just off on the side with the weird arrow.

[slow sierra]

yeah it is

sorry my bad i shouldve clarified

[hollow mesa]

Okay, so do you remember your Pythagorean identities?

[slow sierra]

i think so

[hollow mesa]

So you use them here.

[marsh hatch]

how will that give the tan(x) square part tho in the answer

like im taking the second step aka the one with the arrow and spilting the term

@slow sierra did u get it?

[slow sierra]

im trying but not yet

[hollow mesa]

...you have sine squared.

[slow sierra]

I tried it again today and got the answer

[slow sierra]

thank you

I rlly appreciate it

+close