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derivative of: f(x)= e^x/x^2
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You need to use the quotient rule to evaluate the derivative of the rational function, such that:
`f'(x) = ((e^x)'*x^2 - e^x*(x^2)')/(x^4)`
`f'(x) = (e^x*x^2 - 2x*e^x)/(x^4)`
Factoring out `x*e^x` yields:
`f'(x) = (x*e^x(x - 2))/(x^4)`
Reducing duplicate factors yields:
`f'(x) = (e^x(x - 2))/(x^3)`
Hence, evaluating the derivative of the given function, yields `f'(x) = (e^x(x - 2))/(x^3).`
Posted by sciencesolve on July 9, 2013 at 5:37 PM (Answer #1)
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