# How do you differentiate #y = cos(cos(cos(x)))#?

This is an initially daunting-looking problem, but in reality, with an understanding of the chain rule, it is quite simple.

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To differentiate ( y = \cos(\cos(\cos(x))) ), you can use the chain rule. The derivative is given by:

[ \frac{dy}{dx} = -\sin(x) \cdot \sin(\cos(x)) \cdot \sin(\cos(\cos(x))) \cdot \cos(\cos(\cos(x))) ]

This result is obtained by applying the chain rule repeatedly, from the outside function to the inside functions.

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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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