# How do you differentiate #log_2(x^2sinx) #?

First, I would strongly suggest to use the logarithmic rules to simplify your expression.

Remember the logarithmic rules:

With these rules, you can simplify as follows:

In our case, it means that

holds. Thus, we can transform further:

Now, it's easy to differentiate the first part, and for the second part you just need the chain rule:

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To differentiate the function log base 2 of (x^2 * sin(x)), you would apply the chain rule and the product rule. The derivative is:

[2 * x * sin(x) / (x^2 * sin(x) * ln(2))] + [2 * ln(2) / (x^2 * sin(x))]

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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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