# How do you differentiate #f(x)=x/arcsinsqrt(ln(1/x^2)# using the chain rule?

Well... you definitely need the chain rule for this one!

I would recommend first splitting this up using the quotient rule.

This is where the chain rule comes in. Let's use the following substitutions:

Applying this we get

This gives us

Now, putting in the values we get

This can be simplified to

Putting those in we get

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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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