# How do you find the derivative of #y= ((e^x)/(x^2))#using the quotient rule?

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To find the derivative of ( y = \frac{e^x}{x^2} ) using the quotient rule, differentiate the numerator and denominator separately and apply the quotient rule formula:

[ \frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} ]

Where ( f(x) = e^x ) and ( g(x) = x^2 ). Then, find ( f'(x) ) and ( g'(x) ), and substitute into the quotient rule formula:

[ f'(x) = e^x ] [ g'(x) = 2x ]

Substitute these into the quotient rule formula:

[ y' = \frac{(e^x)(x^2) - (e^x)(2x)}{(x^2)^2} ]

Simplify:

[ y' = \frac{e^xx^2 - 2xe^x}{x^4} ]

[ y' = \frac{e^x(x^2 - 2x)}{x^4} ]

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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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