# What is the derivative of this function #arcsec(x^3)#?

For this you need to know what the derivative of arcsec(x) is.

You can derive it fairly easily:

In the last statement I simplified

If you draw a triangle such that sec(angle) = x, you can understand why it works:

you can see that

Now we know the derivative of arcsec(x) and just need to apply a little chainrule to get our answer:

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Differentiate implicitly:

and:

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The derivative of the function ( \text{arcsec}(x^3) ) with respect to ( x ) is ( \frac{3x^2}{|x^6|\sqrt{x^6-1}} ).

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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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