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

You use the *quotient rule*.

This means that your derivative will look like this

You can simplify this to be

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To find the derivative of ( y = \frac{e^x}{x^2} ), you can use the quotient rule. The quotient rule states that for functions ( u(x) ) and ( v(x) ) where ( v(x) \neq 0 ), the derivative of ( \frac{u(x)}{v(x)} ) is given by:

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

Applying the quotient rule to ( y = \frac{e^x}{x^2} ), where ( u(x) = e^x ) and ( v(x) = x^2 ), we get:

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

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

[ y' = \frac{0}{x^4} ]

[ y' = 0 ]

So, the derivative of ( y = \frac{e^x}{x^2} ) is ( y' = 0 ).

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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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