Calculus question

[3DModelerMan]

Hey, I'm trying to teach myself calculus and I got kind of confused. I'm working on derivatives right now. I know that the derivative is the slope of the tangent line for the graph of the function at a certain point "x". And also that the formula for the derivative is (f(A+deltaA) - f(A) )/ deltaA or well, that's the best I can write without being able to type fraction bars, and I left out the limit. Now suppose I have function f(x) = 2x, (just a simple one for now). Am I supposed to substitute the value of that function with the inputs of the equation for the derivative? Or something else? Also, how do I figure out deltaA? Does it matter what deltaA is? I end up dividing by it again.
Thanks.

[Iyad]

Hi 3DModelerMan,

A is the point were you are trying to calculate the slope of the function.
You should try to calculate this differential when DeltaA go to 0. First of all, u replace A with your value, then you evaluate the limit by using your formula, try to eleminate DeltaA to remove the indetermination; example: supose that your point were you differentiate is 2:

lim(DeltaA->0) (f(2+DeltaA)-f(2))/DeltaA = lim(DeltaA->0) (4+2DeltaA-4)/DeltaA = lim(DeltaA->0) (2) = 2

Heres a tip :
For all linear function, the slope is = to the coefficient of the X.
(ie: d(2x)/dx = 2, d(83275x+532852)/dx = 83275)

For constant function, the slope is always = to zero.

For polynomial functions, (were "a" is an arbitrary constant):
d(x^a)/dx = ax^(a-1)
ex: d(x^0,5)/dx = 0,5*x^-0,5 = 0,5/(x^1/2)

read this, http://en.wikipedia.org/wiki/Derivative
http://en.wikipedia.org/wiki/Derivative ... derivative

[CuteAlien]

Another link I can recommend: http://www.khanacademy.org/
It has a long series about calculus and although I haven't watched his tutorials about derivatives so far, I know that guy usually explains stuff really well.

[3DModelerMan]

Thanks, I understand now.