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

1. nowhereman

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

2. anonymous

no it's $(e^3)(lnx)$

3. 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

4. anonymous

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

5. amistre64

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

6. anonymous

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

7. 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.

8. anonymous

okay, well thank you

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

10. amistre64

i use it on my taxes :)

11. amistre64

a better definition for "e" might be: lim(n->inf) (1 + 1/n)^n right?

12. amistre64

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

13. 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.