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- Thread starter m3dicat3d
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- #1

- Mar 1, 2012

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Imagine the derivative as being the gradient of an expression as per it's first principles. The graph of a the constant $y=a$ is a horizontal line so it has a gradient of $\dfrac{0}{\Delta x} = 0$ so long as $\Delta x \neq 0$.

When you take the derivative of $f(x)$ w.r.t $x$ at a given point P you're evaluating the gradient of f(x) at P, it's a point on a graph rather than a whole graph itself.

Strictly speaking of course the derivative of the natural logarithm is $\dfrac{f'(x)}{f(x)}$ because of the chain rule.

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Thanks for the reply, I just starting writing out a long winded reply as to what I didn't understand, and in the process I thought through the matter more and ended up understanding it haha!

[moderator edit] The discussion regarding the posting issue has been moved here:

http://www.mathhelpboards.com/f25/unable-enter-carriage-return-into-my-posts-4787/

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