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swannyBest ResponseYou've already chosen the best response.0
i got (2x)(e^(1/x))+x^(2)(e^(1/x) which is wrong
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
\[g(x)=e^{\frac{1}{x}}\] \[g'(x)=\frac{1}{x^2}e^{\frac{1}{x}}\] by the chain rule
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
so the second part of your product rule is the problem. first part is good
 one year ago

swannyBest ResponseYou've already chosen the best response.0
but how is it (1/x^2) e^(1/x)?
 one year ago

swannyBest ResponseYou've already chosen the best response.0
shouldn't the derivative e^(1/x)
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
\[y=e^{\frac{1}{x}}\] Let u = 1/x \[\frac{dy}{dx} = \frac{dy}{du}\times \frac{du}{dx} = \frac{d}{du}e^u \times \frac{d}{dx}(\frac{1}{x})= ...?\]
 one year ago

swannyBest ResponseYou've already chosen the best response.0
by quotient rule i did (1)'(x)(1)(x)'/(x)^@
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
You can use power for d/dx (1/x) \[\frac{d}{dx} \frac{1}{x} = \frac{d}{dx} (x^{1}) = (1)x^{11} =...?\]
 one year ago

swannyBest ResponseYou've already chosen the best response.0
ok so it will be e^(x^(2))?
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
The power of e would not change when you differentiate e^(something)!
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
\[\frac{dy}{dx} = \frac{dy}{du}\times \frac{du}{dx} = \frac{d}{du}e^u \times \frac{d}{dx}(\frac{1}{x})= ...?\] u = 1/x and you found d/dx(1/x). So......
 one year ago

swannyBest ResponseYou've already chosen the best response.0
are you asking for the derivative of (1/x) above? i dont understand what exactly you are asking
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
I asked derivative of 1/x because you didn't get that right. To get the derivative of derivative of (x^(2))(e^(1/x)), it should be like this: \[y = x^2e^{\frac{1}{x}}\]\[y' = x^2\frac{d}{dx}e^{\frac{1}{x}} + e^{\frac{1}{x}}\frac{d}{dx}(x^2)\] Then, then you need to work out what d/dx (e^(1/x)) is and d/dx (x^2) are. The later one is easy, and you got that right. The problem is to find d/dx (e^(1/x)) So, let u = 1/x \[\frac{d}{dx}e^{\frac{1}{x}} = \frac{d}{du}(e^u) \times \frac{d}{dx} (\frac{1}{x}) = ...?\]
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Is that clear? Do you understand what we are working on?
 one year ago

swannyBest ResponseYou've already chosen the best response.0
but isn't derivative of (1/x) = x^(2) ? i thought we got that right
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Yes. d/dx (1/x) = x^(2) = 1/x^2
 one year ago

swannyBest ResponseYou've already chosen the best response.0
so you are asking derivative of e^(1/x) * 1/x^2?
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
No. Instead, derivative of e^(1/x), which is equal to e^(1/x) * 1/x^2. Do you understand how to get it?
 one year ago

swannyBest ResponseYou've already chosen the best response.0
so looking at the original question question my answer should be (2x)(e^1/x)(x^2)(e^(1/x))?
 one year ago

swannyBest ResponseYou've already chosen the best response.0
derivative of (x^(2))(e^(1/x)) is the original question
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
No... The second part is not correct. For the second part, you need to find the derivative of e^(1/x). What is it?
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
It is *NOT* e^(1/x) e^(1/x) * 1/x^2 ^How do you get it?
 one year ago

swannyBest ResponseYou've already chosen the best response.0
because derivative of 1/x = 1/x^2
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Yup.. So, can you solve \(y' = x^2\frac{d}{dx}e^{\frac{1}{x}} + e^{\frac{1}{x}}\frac{d}{dx}(x^2)\) now?
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
^That is your derivative btw.
 one year ago

swannyBest ResponseYou've already chosen the best response.0
yes i had already gotten the first part. just the second was the problem
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
Just show us what you've got.
 one year ago

swannyBest ResponseYou've already chosen the best response.0
final answer for the original question is (2x)(e^(1/x))(x^2)(1/x^2)(e^(1/x))
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
That looks pretty cool~ But you can simplify the last term.
 one year ago

swannyBest ResponseYou've already chosen the best response.0
i don't think we have to. but you can show me if you want
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
\[(2x)(e^{\frac{1}{x}})(x^2)\frac{1}{x^2}(e^{\frac{1}{x}}) = (2x)(e^{\frac{1}{x}})\frac{x^2}{x^2}(e^{\frac{1}{x}}) =...?\]
 one year ago

swannyBest ResponseYou've already chosen the best response.0
x^2 / x^2 gets cancelled out = 1
 one year ago

swannyBest ResponseYou've already chosen the best response.0
Thank you very much for your help
 one year ago

swannyBest ResponseYou've already chosen the best response.0
you explain concepts very well
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
You're welcome. I hope I didn't confuse you :S \[(2x)(e^{\frac{1}{x}})\frac{x^2}{x^2}(e^{\frac{1}{x}}) =(2x)(e^{\frac{1}{x}})e^{\frac{1}{x}}=e^{\frac{1}{x}}(2x1)\]That looks nice :)
 one year ago

swannyBest ResponseYou've already chosen the best response.0
No, not confusing at all
 one year ago
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