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How do you find the derivative of # y = x^2e^(-1/x)#?

1 Answer

Aug 4, 2016

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

Explanation:

#y=x^2e^(-1/x)#

By the Product Rule, we get,

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

#=x^2*e^(-1/x)*d/dx(-1/x)+2x*e^(-1/x)#.......[Chain Rule]

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

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

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