I think I see where the confusion is now, irspow, thanks.

]]>The derivative of e^2 would be 2e because the exponent was a constant and you could use the x^n = nx^(n-1) rule.

eh?

e² is a constant, and so d/dx would just be zero...

]]>The derivative of e^2 would be 2e because the exponent was a constant and you could use the x^n = nx^(n-1) rule. This rule is used when a variable is raised to a constant power. Play close attention to what the variable is in the equation. Look around the internet for rules for differentiation of logarithmic functions and you will see where you went wrong.

]]>e^2

we know the differential of e^x = e^x dx so the slope of the line at 2 is e^2

But what if we used the fact that the derivative of x^n = nx^(n-1) ?

by this definition the derivative of e^2 should be ne^1 or 2e^1 but this is different then e^2!

So what if you took the derivitive of n^2 and n just happens to equal e or close to it? Would the derivative be wrong?

This is disturbing.

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