设\(y = \arcsin x\)，则\(x = \sin y\)，对\(x = \sin y\)求导得\(x^\prime=\cos y\)，根据反函数导数公式\(y^\prime = \frac{1}{x^\prime}\)，所以\((\arcsin x)^\prime=\frac{1}{\cos y}\)。又因为\(\cos y = \sqrt{1 - \sin^{2}y}\)，而\(x = \sin y\)，所以\(\cos y=\sqrt{1 - x^{2}}\)，那么\((\arcsin x)^\prime=\frac{1}{\sqrt{1 - x^{2}}}\)。 <a...

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