# Find the derivative using logarithmic differentiation?

Pose:

Then:

and:

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Take the natural log of both sides.

Take the derivative of both sides.

Multiply both sides by

I'm not here to judge, but I noticed this is the second logarithmic differentiation problem I have answered for you. Perhaps, you should try to better understand logarithmic differentiation. It is actually quite simple.

Here is a helpful video if you are interested in learning more.

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Use the natural logarithm on both sides:

Differentiate both sides:

The left side requires the use of the chain rule:

The right side requires the use of the product rule:

The second term simplifies:

Multiply both sides by y:

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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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