# How do you find the derivative of #y = 6 cos(x^3 + 3)# using the chain rule?

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To find the derivative of ( y = 6 \cos(x^3 + 3) ) using the chain rule, follow these steps:

- Identify the outer function, which is ( \cos(u) ), where ( u = x^3 + 3 ).
- Differentiate the outer function with respect to its inner function ( u ), which gives ( -\sin(u) ).
- Multiply the result by the derivative of the inner function ( u ) with respect to ( x ), which is ( \frac{d}{dx}(x^3 + 3) = 3x^2 ).

So, applying the chain rule, the derivative of ( y ) with respect to ( x ) is:

[ \frac{dy}{dx} = -6\sin(x^3 + 3) \cdot 3x^2 = -18x^2 \sin(x^3 + 3) ]

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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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