anonymous
  • anonymous
the derivative of y=e^3 ln x
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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nowhereman
  • nowhereman
If you mean \[y=e^{3\ln x}\] use power rules to eliminate e and ln
anonymous
  • anonymous
no it's \[(e^3)(lnx)\]
amistre64
  • amistre64
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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anonymous
  • anonymous
oh, just as if the number 2 was in place of e^3? I would just leave it? oh, okay thanks
amistre64
  • amistre64
yep..... that e may look like a variable, but its just like "pi" in the sense thatits stands for an actual number :)
anonymous
  • anonymous
but how would you know if it's a constant? Because originally I used the product rule.
amistre64
  • amistre64
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.
anonymous
  • anonymous
okay, well thank you
nowhereman
  • nowhereman
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.
amistre64
  • amistre64
i use it on my taxes :)
amistre64
  • amistre64
a better definition for "e" might be: lim(n->inf) (1 + 1/n)^n right?
amistre64
  • amistre64
whcih of course is whats up there lol..... gotta quit glossing over stuff
nowhereman
  • nowhereman
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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