Question

the derivative of y=e^3 ln x

Answer 1

If you mean \[y=e^{3\ln x}\] use power rules to eliminate e and ln

Answer 2

no it's \[(e^3)(lnx)\]

Answer 3

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

Answer 4

oh, just as if the number 2 was in place of e^3? I would just leave it? oh, okay thanks

Answer 5

yep..... that e may look like a variable, but its just like "pi" in the sense thatits stands for an actual number :)

Answer 6

but how would you know if it's a constant? Because originally I used the product rule.

Answer 7

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.

Answer 8

okay, well thank you

Answer 9

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 \[e^x = \lim_{n→∞}(1+\frac x n)^n = \sum_{n=0}^∞ \frac{x^n}{n!}\] expanding it to complex numbers you get \[e^{iπ} + 1 = 0\] So it really is a pretty amasing number.

Answer 10

i use it on my taxes :)

Answer 11

a better definition for "e" might be:

lim(n->inf) (1 + 1/n)^n right?

Answer 12

whcih of course is whats up there lol..... gotta quit glossing over stuff

Answer 13

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.