Prove that `(d)/(dx)(sin^(-1)x)=(1)/(sqrt(1-x^(2))`, where `x in [-1,1].`

Explanation

To prove that \(\frac{d}{dx}(\sin^{-1}x) = \frac{1}{\sqrt{1-x^2}}\), where \(x \in [-1, 1]\), we can follow these steps:

### Step 1: Let \(y = \sin^{-1}(x)\)
We start by letting \(y\) be the inverse sine of \(x\):
\[ y = \sin^{-1}(x) \]

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