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swanny
 2 years ago
derivative of (x^(2))(e^(1/x))
swanny
 2 years ago
derivative of (x^(2))(e^(1/x))

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

satellite73
 2 years ago
Best 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0so the second part of your product rule is the problem. first part is good

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

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0shouldn't the derivative e^(1/x)

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

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0by quotient rule i did (1)'(x)(1)(x)'/(x)^@

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

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0ok so it will be e^(x^(2))?

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3The power of e would not change when you differentiate e^(something)!

Callisto
 2 years ago
Best 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......

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3I 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 \[\frac{d}{dx}e^{\frac{1}{x}} = \frac{d}{du}(e^u) \times \frac{d}{dx} (\frac{1}{x}) = ...?\]

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3Is that clear? Do you understand what we are working on?

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3Yes. d/dx (1/x) = x^(2) = 1/x^2

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

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

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

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

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

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

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0because derivative of 1/x = 1/x^2

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3^That is your derivative btw.

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0yes i had already gotten the first part. just the second was the problem

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3Just show us what you've got.

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

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3That looks pretty cool~ But you can simplify the last term.

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0i don't think we have to. but you can show me if you want

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

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0x^2 / x^2 gets cancelled out = 1

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you very much for your help

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0you explain concepts very well

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3You'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 :)

swanny
 2 years ago
Best ResponseYou've already chosen the best response.0No, not confusing at all
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