# How do you find the derivative of #sinx/e^x#?

Substituting these values into (A)

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To find the derivative of ( \sin(x)/e^x ), we use the quotient rule. The quotient rule states that if we have a function of the form ( f(x) = \frac{g(x)}{h(x)} ), then the derivative of ( f(x) ) is given by ( f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} ). Applying this rule to our function, with ( g(x) = \sin(x) ) and ( h(x) = e^x ), we have ( g'(x) = \cos(x) ) and ( h'(x) = e^x ). Plugging these values into the formula, we get:

[ \frac{d}{dx} \left( \frac{\sin(x)}{e^x} \right) = \frac{\cos(x)e^x - \sin(x)e^x}{(e^x)^2} ] [ = \frac{e^x(\cos(x) - \sin(x))}{e^{2x}} ] [ = \frac{\cos(x) - \sin(x)}{e^x} ]

So, the derivative of ( \sin(x)/e^x ) is ( (\cos(x) - \sin(x))/e^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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