# How do you find the 108th derivative of #y=cos(x)# ?

Modulus 4 will return either 0, 1, 2, or 3. Rather than performing 108 derivatives, we need to calculate 108 modulus 4; this equals 0. Although remainder works for positive dividends, it's best to become accustomed to modulus because this works for negative dividends.

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To find the 108th derivative of ( y = \cos(x) ), we can use the fact that the derivative of ( \cos(x) ) is ( -\sin(x) ), and the derivative of ( -\sin(x) ) is ( -\cos(x) ). This pattern repeats every fourth derivative.

Since the 108th derivative is divisible by 4, the derivative will be ( \cos(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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