# How do you differentiate #arcsin(csc(x^3)) )# using the chain rule?

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To differentiate arcsin(csc(x^3)) using the chain rule, follow these steps:

- Start with the outer function, arcsin(u), where u = csc(x^3).
- Find the derivative of the outer function: d(arcsin(u))/du = 1/sqrt(1 - u^2).
- Now, apply the chain rule by finding the derivative of the inner function.
- The inner function is u = csc(x^3), so its derivative is du/dx = -3x^2 * csc(x^3) * cot(x^3).
- Finally, multiply the derivative of the outer function by the derivative of the inner function to get the overall derivative: = (1/sqrt(1 - u^2)) * (-3x^2 * csc(x^3) * cot(x^3)).

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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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