The First Derivative. Some help?

[jay7]

Well, I've been given this wonderful formula to use

Æ’(x + h) -Æ’(x) /h (the entire thing divided by h..)

So, that's nice and easy, and substituing and expanding the formula is as well, except now I have been told to expand it with something other than
Æ’(x) = ax^2 + bx + c, here are the homework questions that I don't have a clue as to do..

1.) Æ’(x+h) ^(1/x) - Æ’(x) /h
Now, my first instinct is to make the Fraction Exponent not a fraction, by making it ^x-1 however, then I don't know what to do from there either?

2.) Æ’(x+h) ^square root of x -Æ’(x) /h
So then I think, ok...get rid of the root...Perhaps square the entire thing, and then see where it takes me? Is that legal in this little world?

3.) Æ’(x+h) ^ c times g(x) - Æ’(x) /h
Yeah...

I'd ask the teacher, but every time I do during class it just takes to damn long (exchange student remeber..) so then I try at the end of class, where we don't have enough time... So, could one of you mathematically inclined individuals help me out

Thanks ..Hopefully I don't have to make to many of these threads.

[Colin]

I don't understand what's happening here.

Are the questions to find the derivative of functions by using that formula?

Ie:

f(x)=3x, so f(x+h)=3(x+h)=3x+3h

then f(x+h)-f(x) = 3x + 3h - 3x = 3h

so [f(x+h)-f(x)]/h = 3h/h = 3 (square brackets don't mean anything different, just for visibility)


f(x) = 3x -> f'(x) = 3


If so, there's no reason why you would end up with things like the examples you've listed. What are the functions that lead you to these messes?

[jay7]

See that is the thing, Putting something into that formula would only make to much sense, but the teacher is giving us an awkward formula, and then telling us to expand it...Or so I think... So multiply Æ’(x+h) ^(1/x) - Æ’(x) /h out...But I haven't got the slightest clue how to multiply out with 1/x as the exponent..

I hate not understanding math,..