the derivative of y=e^3 ln x

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the derivative of y=e^3 ln x

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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If you mean \[y=e^{3\ln x}\] use power rules to eliminate e and ln
no it's \[(e^3)(lnx)\]
e^3 is jsut a constant so like any constant put it aside and derive ln(x) D(ln(x)) = 1/x now bring the constant back to it... e^3 --- x

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oh, just as if the number 2 was in place of e^3? I would just leave it? oh, okay thanks
yep..... that e may look like a variable, but its just like "pi" in the sense thatits stands for an actual number :)
but how would you know if it's a constant? Because originally I used the product rule.
There is this guy in mathmatics calle Euler. and he has a special number that pops up alot in natural stuff.. 2.71828182845905....... or something like that. So whenever you see an "e" being used in an equation, they are representing Eulers number.
okay, well thank you
Well, it pops-up a lot in mathematics too ^^. \[f(x) = e^x\] is the solution to the initial-value problem \[f'(x) = f(x)\] and also \[e^x = \lim_{nā†’āˆž}(1+\frac x n)^n = \sum_{n=0}^āˆž \frac{x^n}{n!}\] expanding it to complex numbers you get \[e^{iĻ€} + 1 = 0\] So it really is a pretty amasing number.
i use it on my taxes :)
a better definition for "e" might be: lim(n->inf) (1 + 1/n)^n right?
whcih of course is whats up there lol..... gotta quit glossing over stuff
Hehe, there so many ways to define it :-) Yet another would be to first define \[\ln x = \int_1^x \frac 1 x\] and then say e^x is the inverse function.

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