Question

Differentiate following with respect to x.
a) e^1/3x

Answer 1

@zzr0ck3r

Answer 2

\[\large \frac{ d }{ dx } e^{\frac{ x }{ 3 }}?\]

Answer 3

I don't know..I'm new to this..

Answer 4

hes asking you to clarify what function you mean to differentiate.

Answer 5

its hard to tell without parentheses

Answer 6

ok

Answer 7

Well is your expression \[\huge e^\frac{ 1 }{ 3x }~~~~\text{or}~~~e^ \frac{ x }{ 3 }\]

Answer 8

or

\(e^\frac{1}{3}x\)

Answer 9

LHS

Answer 10

@iambatman has got you, I got to go eat ;)

Answer 11

Ah ok cool so when you differentiate e^x you get the result of e^x, kind of crazy right? Since I am assuming you're sort of new to the notation of derivatives I will use "prime" meaning differentiate and it denoted as `'` \[\huge (e^{\frac{ 1 }{ 3 }x})'\] that little apostrophe represents we have to get the derivative.
So we can use the "chain rule" here assuming you've learned this already, so the process would go sort of like this:
\[\huge (e^{\frac{ 1 }{ 3 }x})' \implies \frac{ 1 }{ 3 }e^{\frac{ x }{ 3 }} \]

Answer 12

iambatman after you are done with this question could you help me??

Answer 13

I guess to show the whole process with the "fancy" notation you would let u=x/3
\[\frac{ d }{ dx }(e^{x/3}) = \frac{ de^u }{ du }\frac{ du }{ dx }\] where u = x/3, d/du e^u = e^u as I mentioned the derivative of e^x = e^x, so \[e^{x/3}\left( \frac{ d }{ dx }\left( \frac{ x }{ 3 } \right) \right) \implies \frac{ 1 }{ 3 }\left( \frac{ d }{ dx }x \right)e^{x/3} \implies \frac{ 1 }{ 3 }e^{x/3}\] since the 1/3 is a constant just factor it out. and derivative of x is just 1.

Answer 14

If you don't understand a certain part just ask, I can explain it, it can look messy I guess.

Answer 15

Ok

Answer 16

Understood.
Thanks @iambatman

Answer 17

Np, glad you could understand!