# What is the derivative of #log_3((xsqrt(x-1))/2)#?

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Use the following Properties of Logarithm to expand the problem before taking derivatives.

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The derivative of ( \log_3\left(\frac{x\sqrt{x-1}}{2}\right) ) is ( \frac{1}{x\ln(3)} \cdot \frac{\sqrt{x-1}}{2} \cdot \left(1 + \frac{1}{2(x-1)}\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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