# How do you find the derivative of #arcsin(x^2)#?

Differentiating wrt x;

And so;

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To find the derivative of arcsin(x^2), you can use the chain rule. Let y = arcsin(x^2).

- Find the derivative of y with respect to x: dy/dx = d(arcsin(u))/du * du/dx, where u = x^2.
- Compute the derivatives:
- d(arcsin(u))/du = 1 / sqrt(1 - u^2)
- du/dx = 2x

- Substitute the derivatives back into the chain rule formula.
- Simplify the expression to get the final derivative.

Therefore, the derivative of arcsin(x^2) with respect to x is dy/dx = (2x) / sqrt(1 - (x^2)^2).

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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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