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I'm in Pre-Calculus this semester and it's going swimmingly and I thought I'd try and get ahead for Calc I, which I plan on taking this summer. Anyways, all I have really to go off of right now is "How to Ace Calculus: The Streetwise Guide", my brain, and wikipedia. I'm struggling to find more problems to work on (the guide is good in explaining, but I'd like more practice) and I worry that if I just start making up equations to practice finding the derivative that I might end up teaching myself the wrong methods. Here is an example I just came up with off the top of my head. When I tried to check my answer I came up with a few possibilities...

Find Derivative:

f(x) = X^-3

2. Relevant equations

Power Rule

3. The attempt at a solution

I get:

[tex] \frac {-3}{x^4} [/tex]

However when I plug it into various "derivative calculators" online I get 0 or some other random solution (one told me the derivative of X=0). Are the calculators wrong? Am I wrong? Is there some way I can check my answers by hand? What I'm doing right now is graphing both the derivative and the original function on my graphing calculator (TI-84 Plus if it makes any difference) and then plugging in a number for X in the equation I got for the derivative and seeing if A) that point indeed exists for that equation and B) if the number agrees with the slope of the original graph. For example, if I plug in x=1 in the derivative I get -3, which is a point on the graph of the derivative and the slope is negative in the original graph( f(x)=x^-3) at the point x=1. I guess my question is am I doing it right? Is there anything I can do to improve my method?

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# Homework Help: Derivatives: Checking your work, how?

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