# How do you differentiate # g(x) =sin^2(x/6) #?

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To differentiate ( g(x) = \sin^2(x/6) ), you can use the chain rule.

First, differentiate the outer function (\sin^2(x/6)) with respect to its inner function (x/6), which is (\sin(u)) where (u = x/6). The derivative of (\sin^2(u)) with respect to (u) is (2\sin(u)\cos(u)).

Then, multiply by the derivative of the inner function with respect to (x), which is (1/6).

So, the derivative of ( g(x) = \sin^2(x/6) ) is ( g'(x) = \frac{1}{6} \cdot 2\sin\left(\frac{x}{6}\right) \cos\left(\frac{x}{6}\right) ).

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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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