# What is the derivative of this function #y=csc^-1(4x^2)#?

Now, using:

Now simplify:

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The derivative of the function ( y = \csc^{-1}(4x^2) ) with respect to ( x ) is:

[ \frac{dy}{dx} = -\frac{8x}{|x|\sqrt{16x^4-1}} ]

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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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