# How do you find the derivative of #y= cos^3 w + cos(w^3)#?

so

Now we've split it up, we can tackle each term separately.

The product rule states that

so

therefore,

Now we can begin to look at the second term, for which we need the chain rule:

so

Now we can put the whole thing back together,

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To find the derivative of (y = \cos^3(w) + \cos(w^3)), you would use the chain rule and the derivative of cosine function. The derivative would be:

[y' = -3\cos^2(w) \sin(w) - \sin(w^3) \cdot 3w^2 \sin(w^3 - 3\cos(w^3) \cdot w^2\sin(w^3 - w^2)]

Alternatively, you can express the derivative as:

[y' = -3\cos^2(w) \sin(w) - 3w^2\sin(w^3) \sin(w^3) - 3\cos(w^3)w^2\sin(w^3 - w^2)]

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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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