# How do you find the derivatives of #y=log_2(3x)#?

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To find the derivative of ( y = \log_2(3x) ), you can use the chain rule for differentiation.

First, differentiate the outer function (\log_2(u)), treating the inner function (u = 3x) as a whole. Then, multiply it by the derivative of the inner function.

The derivative of (\log_2(u)) with respect to (u) is (\frac{1}{u \ln 2}).

The derivative of (u = 3x) with respect to (x) is (3).

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

[ y' = \frac{1}{3x \ln 2} \times 3 = \frac{1}{x \ln 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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