# How do you find the derivative of #y= cos(x)/x^8#?

Use the quotient rule, which states that, for this problem,

The two derivatives are:

Plugging these both back in, we see that

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To find the derivative of ( y = \frac{\cos(x)}{x^8} ), you can use the quotient rule, which states that for functions ( u(x) ) and ( v(x) ), the derivative of ( \frac{u(x)}{v(x)} ) is given by ( \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2} ). Applying this rule to ( y = \frac{\cos(x)}{x^8} ), the derivative is:

[ y' = \frac{-x^8 \sin(x) - 8x^7 \cos(x)}{(x^8)^2} ]

Simplifying further:

[ y' = \frac{-x^8 \sin(x) - 8x^7 \cos(x)}{x^{16}} ]

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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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