Question

For \[y=\sin^{-1}x\], which relation uses \[y_{1}\] for the first derivative?

Options

• \[(1-x^2)y_{1}=1\]

• \[(1-x^2)y_{2}^{2}=1\]

• \[(1-x^2)y_{2}=1\]

• \[(1-x^2)y_{1}^{2}=1\]

Answer 1

Here \[y_{1}=\frac{1}{\sqrt{1-x^2}}\]. Squaring this identity gives \[y_{1}^{2}=\frac{1}{1-x^2}\], hence \[(1-x^2)y_{1}^{2}=1\].