The derivative of sin−1⁡x w.r.t. cos−1⁡1−x2 is.

y=sin−1⁡x, z=cos−1⁡1−x2=sin−1⁡x∴ y=z ⇒ dydz=1

The derivative of sin−1⁡x w.r.t. cos−1⁡1−x2 is.

y=sin−1⁡x, z=cos−1⁡1−x2=sin−1⁡x∴ y=z ⇒ dydz=1

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The derivative of $\sin^{- 1} x w.r.t. \cos^{- 1} \sqrt{(1 - x^{2})}$ is.

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$1 / (1 - x^{2})$

$c {os}^{- 1} x$

none

answer is C.

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$\begin{array}{l} y = \sin^{- 1} x, \\ z = \cos^{- 1} \sqrt{(1 - x^{2})} = \sin^{- 1} x \end{array}$

$∴ y = z \Rightarrow \frac{d y}{d z} = 1$

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The derivative of sin−1⁡x w.r.t. cos−1⁡1−x2 is.

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The derivative of $\sin^{- 1} x w.r.t. \cos^{- 1} \sqrt{(1 - x^{2})}$ is.