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What is the derivative of #f(x)=(e^(1/x))/x^2# ?

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Sep 20, 2014

By Quotient Rule,

#f'(x)={-1/x^2e^{1/x}cdot x^2-e^{1/x}cdot2x}/{(x^2)^2}#

by cancelling out #x^2# in the numerator,

#={-e^{1/x}-2xe^{1/x}}/{x^4}#

by factoring out #-e^{1/x}# from the numerator,

#=-{(1-2x)e^{1/x}}/{x^4}#

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