Question

Differentiate with respect to x:

e^(3lnx)

Answer 1

Chain rule.. you know it? :)

Answer 2

yes, but how??

Answer 3

my question was, does e^ln cancel out here?

Answer 4

:Whoops
I am shamed for not noticing that :D
sorry, do the cancellation first

Answer 5

so what does that become, 3x??

Answer 6

No... remember the properties of logarithms :)
\[\huge p \ln x = \ln x^p\]

Answer 7

or should i do the whole f'(x)e^f(x) thing??

Answer 8

That was what I thought, until you reminded me that e^x and ln x cancel out :)
See that exponent
\[\huge 3 \ln x\]
How can you use that property that I showed you?

Answer 9

OMG

Answer 10

Stuck? Something wrong?

Answer 11

I'M AN IDIOT
THANK YOU FOR POINTING OUT MY IDIOCY OMG :P

Answer 12

SO SIMPLE

Answer 13

YOU pointed out my idiocy XD

Answer 14

So what's your answer? :D

Answer 15

yuck. we suck :P

Answer 16

3x^2 :D

Answer 17

LOL yeah. Now, for entertainment purposes, let's see what happens if we apply the chain rule...
\[\huge \frac{d}{dx}e^{3\ln x}=e^{3lnx}\frac{d}{dx}3\ln x=\frac{3e^{3\ln x}}{x}\]
You'd have to simplify the exponential anyway.
ANYWAY
Great job :)

Answer 18

omg thats scary looking.
Well, it's easier than implicit.
Actually, implicit's pretty easy :P

Answer 19

and omg thank you SO much. stick around, there are some more questions coming up :)

Answer 20

Sure :)

Answer 21

ok. y = \[x^2\ln (1/x)\]

Answer 22

where x is the ratio of the inner radius to outer radius. the inner radius is 1/2. for max speed, what should be the outer radius?

Answer 23

I've got the answer, i just wanna double check. i have \[\sqrt{e}/2\]

Answer 24

I honestly don't know what these mean :)
What's an inner radius?

Answer 25

arrey, imagine a sphere. or say, the earth. so the radius of the core, and the radius of the mantle so to speak.

Answer 26

Okay...