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anonymous
 5 years ago
the derivative of y=e^3 ln x
anonymous
 5 years ago
the derivative of y=e^3 ln x

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nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0If you mean \[y=e^{3\ln x}\] use power rules to eliminate e and ln

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no it's \[(e^3)(lnx)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0e^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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, just as if the number 2 was in place of e^3? I would just leave it? oh, okay thanks

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep..... that e may look like a variable, but its just like "pi" in the sense thatits stands for an actual number :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but how would you know if it's a constant? Because originally I used the product rule.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0There 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.

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Well, it popsup a lot in mathematics too ^^. \[f(x) = e^x\] is the solution to the initialvalue problem \[f'(x) = f(x)\] and also \[e^x = \lim_{n→∞}(1+\frac x n)^n = \sum_{n=0}^∞ \frac{x^n}{n!}\] expanding it to complex numbers you get \[e^{iπ} + 1 = 0\] So it really is a pretty amasing number.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i use it on my taxes :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0a better definition for "e" might be: lim(n>inf) (1 + 1/n)^n right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0whcih of course is whats up there lol..... gotta quit glossing over stuff

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Hehe, 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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