Antiderivatives

Limits, differentiation, related rates, integration, trig integrals, etc.
GreenLantern
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Antiderivatives

Postby GreenLantern » Tue Apr 12, 2011 9:51 pm

Okay, so F(x) is the anti derivative and f(x) is the normal whatever you want to call it.
The e's and ln's have always given me problems, I just don't understand them.









My work:
Take derivative
Now use the chain rule
Now I'm stuck, I just have no idea how to multiply those together; otherwise I'm pretty sure I got this one.

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stapel_eliz
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Postby stapel_eliz » Tue Apr 12, 2011 11:25 pm

GreenLantern wrote:The e's and ln's have always given me problems, I just don't understand them.

Do you mean that your algebra classes never covered the natural logarithm and the natural exponential? :confused:

GreenLantern
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Re: Antiderivatives

Postby GreenLantern » Wed Apr 13, 2011 2:00 pm

I have covered both, but I can't ever remember the rules about them... I usually end up looking them up and learning them again (with varying success) every time I need them.



My work:

If I'm not mistaken, I'm using the product rule because xlnx is to weird to derive from.
Simplify...
Derive?
Yes!? Point for me? It looks right...

On to round 2...


I think I'm doing the same thing? But I don't know how I'll end up with the (1+x)

That seriously looks wrong... I don't know what rule I'm using to split the xe^x and that's what I think I'm getting stuck on.

Again, the root fraction question.


My work:
Take derivative
Now use the chain rule
Is this yet another (longer) product rule?
I think that made it worse. Unless I simplify?
I realized I can simplify sooner?
Second try:
Take derivative
Now use the chain rule
Simplify
Didn't help.

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Martingale
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Re: Antiderivatives

Postby Martingale » Wed Apr 13, 2011 10:55 pm

GreenLantern wrote:On to round 2...


I think I'm doing the same thing? But I don't know how I'll end up with the (1+x)

That seriously looks wrong... I don't know what rule I'm using to split the xe^x and that's what I think I'm getting stuck on.





factor out an

GreenLantern wrote:Again, the root fraction question.


My work:
Take derivative
Now use the chain rule
Is this yet another (longer) product rule?
I think that made it worse. Unless I simplify?
I realized I can simplify sooner?
Second try:
Take derivative
Now use the chain rule
Simplify
Didn't help.




now simplify


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