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How do you differentiate #y=e^-x/x#?

1 Answer

Oct 21, 2016

# dy/dx = (-e^-x(x+1)) / x^2 #

Explanation:

You need to use the quotient rule; # d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 #

so, # dy/dx = (xd/dx(e^-x)-e^-xd/dx(x)) / x^2 #

# :. dy/dx = (x(-e^-x)-e^-x(1)) / x^2 #

# :. dy/dx = (-xe^-x-e^-x) / x^2 #

# :. dy/dx = (-e^-x(x+1)) / x^2 #

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