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

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To find the derivative of ( y = x^2(e^{-1/x}) ), you can use the product rule and chain rule. The product rule states that if you have two functions, ( u(x) ) and ( v(x) ), their derivative is ( u'(x)v(x) + u(x)v'(x) ). Here, ( u(x) = x^2 ) and ( v(x) = e^{-1/x} ). The derivatives of ( u(x) ) and ( v(x) ) are ( u'(x) = 2x ) and ( v'(x) = e^{-1/x} \cdot \frac{1}{x^2} ), respectively. Applying the product rule, the derivative of ( y ) is:

[ y' = (2x)(e^{-1/x}) + (x^2)\left(e^{-1/x} \cdot \frac{-1}{x^2}\right) ] [ y' = 2xe^{-1/x} - \frac{e^{-1/x}}{x} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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