CAA: Christian Anime Alliance

So, yeah. I hate this stuff.

Anyways, guys, I am so confused. Right now, we're talking about implicit differentiation, and I'm completely lost. The problem I'm trying to work through is 2^2+[square root of (st)]+2t^3-5t=0. I'm supposed to find velocity ds/dt. How on earth do I do that? 0__o Please, help me, someone.

Yay calculus!

If you take the problem and differentiate by t it becomes:

(4+(st)^(1/2)+t^3-5t)dt=0dt

which becomes (using the product rule)

(1/2)*(st)^(-1/2)*(t*(ds/dt)+s))+3t^2-5=0

solving for ds/dt you get

ds/dt=(3*t^2-5*(st)^(1/2))*2+s

now you just need to solve the original equation for s (using algebra) and plug that solution into this equation. It's going to be a bit messy, but from this point on it's more messy algebra than any difficult calculus

Now, if you're confused about the product rule (i.e. if you have to differentiate two things multiplied by each other) it goes like this:

d(u*v)/dx=du/dx*v+dv/dx*u

Also, you could be having problems with differentiating (s*t)^1/2. In that case, the rule is d((u*v)^w)/dx = d(y^w)/dx where y=u*v. d(y^w)/dx = w*(y^(w-1))*dy/dx

I hope that helps! I'd be happy to try to give you more advice, but I think you can take it from here.

O.O

29 minutes. Wow Puritan. Just... Wow.

That does help. Except I screw up. The equation was actually 2s^2+[the square root of (st)]-4=3t

Sorry!

Mangafanatic wrote:That does help. Except I screw up. The equation was actually 2s^2+[the square root of (st)]-4=3t

Sorry!

Oh wow. I think Osaka needs a proof-reading tutorial instead of a calculus one. That's terrible.

Yumie wrote:Oh wow. I think Osaka needs a proof-reading tutorial instead of a calculus one. That's terrible.

Hey. No picking on me. I've been working on Calculus for 2 hours and I've gotten NOTHING done. Yeah. I'm somewhat. . . irked.

Mangafanatic wrote:That does help. Except I screw up. The equation was actually 2s^2+[the square root of (st)]-4=3t

Sorry!

Yeah, sure. That was just the next question!

2*2(s ^1) * ds/dt + 1/2*(st)^(-1/2) * (ds/dt * t + s * dt/dt) = 3*dt/dt

=> 4s * ds/dt + (ds/dt *t + s)/(2 * (st) ^ (1/2) = 3

The rest is left as an exercise for the reader.

Warrior4Christ wrote:Yeah, sure. That was just the next question!

She wouldn't do that. She's a good girl. Well, except for that time with the limo and the robot-hampster. I *still* can't get the ketchup stains out of my tux.

Warrior4Christ wrote:The rest is left as an exercise for the reader.

Classic.

Mithrandir wrote:O.O

29 minutes. Wow Puritan. Just... Wow.

*looks left* *looks right* Can you keep a secret?
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For some odd reason, I really love calculus. I can't explain it, but I really like it. When I saw this post I was oddly thrilled to be able to help someone solve a calculus problem. I admit, I'm a nutty engineer, but at least I'm easy to please...

Puritan wrote:*looks left* *looks right* Can you keep a secret?
...
...
For some odd reason, I really love calculus. I can't explain it, but I really like it. When I saw this post I was oddly thrilled to be able to help someone solve a calculus problem. I admit, I'm a nutty engineer, but at least I'm easy to please...

So, when I take calculus next year, I know who go to to ask questions. . .

YUS!!!

i would have to agreee with you the calc is fun...once you get the hang of it, make sure you know what is going on though before you move on...though it may take more time it makes things alot easyer