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anonymous
 4 years ago
Derivative help.
anonymous
 4 years ago
Derivative help.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=d%2Fdx+%28cosx%29%2Fe%5Ex%29 this should give your answer.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1Dx(cos(x)*e^(x)) and product rule it

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah, either use the product rule or the quotient rule (which in fact are equivalent)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I got the answer but it's different what khanAcademy is showing me, so please give me the exact answer so that i can verify it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0d/dx((cos(x))/e^x) = e^(x) (sin(x)+cos(x))

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1cos'(x)*e^(x) + cos(x)*e'^(x) sin(x)*e^(x)  cos(x)*e^(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d}{dx} \left(\frac{\cos (x)}{e^x}\right) = \frac{d}{dx} e^{x}\cos (x) = e^{x}(\sin (x)) + \cos (x)(e^{x}) = e^{x} (\sin (x) + \cos (x))\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hmm it wrote it off the page

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d}{dx} \left(\frac{\cos (x)}{e^x}\right) = \frac{d}{dx} e^{x}\cos (x)\] \[ = e^{x}(\sin (x)) + \cos (x)(e^{x})\] \[ = e^{x} (\sin (x) + \cos (x))\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0In the second step why the second term is e^x, why you did not derviate it ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the derivative of \[e^{x}\] is \[e^{x}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but i learned the derivative of e^x is e^x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0this is what khan academy says the answer is

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes that's right. Let's show, usin gthe chain rule that the derivative of e^{x} is e^{x}. Find the derivative of \[y = e^{x}. \] Let t=x. Then y = e^t \[\frac{dy}{dx} = \frac{dy}{dt}\frac{dt}{dx} = e^{t}(1) = e^{x}(1) = e^{x}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes, notice that answer a) is exactly the same as \[e^{x} (\sin (x) + \cos (x))\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That answer is likely derived from the quotient rule, which can be rewritten as the product rule by making the requirement of multiplying by e^{x} rather than dividing by e^x. Notice that this is equivalent.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thanks a lot, i understood it.
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