Thread: Fun for the brain

Ok please don't google anything, if you do then your conscience will make you feel bad.

If you memorise this from school that's great, but if you have forgotten, then work it out.

What is the derivative of at point x₀?
What is the derivative of at point x₀?


AGAIN! NO GOOGLING!

The first person to answer wins!

Since when was calculus fun? Just kidding. Lucky me I'm on the forum right now. I haven't taken a real calculus class yet, so I could be wrong, but let me try. Attempts follow in orange (see edit)...

The derivative of with respect to , so I'm finding
For this, I will assume , , and are unspecified constants, and not actual variables (is there a difference?).
I'll just treat the 3 terms individually thanks to the sum rule.
Well, is a constant, so that can be "discarded".
is simply a constant coefficient so now I have
And for I'll use the constant multiple rule and differentiate the power function, so I have
Finally, I'll say

As for the other problem, for , it's something they just tell you to remember (yeah it's ). I tried to do it anyway using the limit definition but I got stuck. I tried different ways using substition, trig identities, and all that and I still couldn't get it! I saw it done a while ago on an MIT lecture video but I forgot how the professor did it. So I'm stumped on this one.

Edit: Apparently, Tex won't work in a different color so I'm just changing what I can to orange.

P.S. You said the first person to answer wins. You didn't specify if they had to be right or wrong, just that they had to answer. Do I get a prize?

P.P.S. Check out my thread about paper games. No one's solved the latest one as of now.

Originally Posted by Wise Man

What is the derivative of at point x₀?

Therefore



Evaluate at x₀ to obtain the answer

Originally Posted by Wise Man

What is the derivative of at point x₀?

Evaluate at x₀ to obtain the answer



What do I win?

heheh well you get nothing... Ya this isn't really that fun...

halorealm you got stuck? Take a look at this: sin(x)/x = 1 when x gets closer to 0. That will help you maybe.

Um the winner is... myself because I 'answered' first.

Other people who posted:

Originally Posted by Wise Man

Um the winner is... myself because I 'answered' first.

Oh no you don't! You didn't answer at all. You merely posted the question. We have no evidence which supports the assertio that you knew the answer before you posted the question.

Originally Posted by Wise Man

Um the winner is... myself because I 'answered' first.

Au contraire, you are the inquirer. You answered nothing.

sin(x)/x = 1 when x gets closer to 0

I'm aware of that limit but... hmm, I'll just have to take a look at that video again. But for someone who hasn't taken trigonometry or calculus yet, I'd say I did alright.

Ok fine fine both of you win, happy?

No.

Oh, and I finally remembered how to do the difference quotient approach for . After my first attempt, I tried a few more times, still to no avail. So I just watched the MIT video again and now I finally get it.

I don't see how doing regular calculus derivatives is fun for the brain lol

Agreed. No offense in any way Wise Man It's just terribly ironic in a funny way.

Anyway, in all seriousness, I heard delta-epsilon limits mentioned *shivers* I've always wondered how doing limit differentiation that way is like. Never done it.