# What is the derivative of #f(x)=7 arcsin(x^2)#?

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The derivative of ( f(x) = 7 \arcsin(x^2) ) is:

[ f'(x) = \frac{d}{dx} (7 \arcsin(x^2)) = \frac{7}{\sqrt{1 - x^4}} \cdot 2x ]

Simplified:

[ f'(x) = \frac{14x}{\sqrt{1 - x^4}} ]

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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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