If \(y = e^{\sin^{-1} x}\), \(-1 \lt x \lt 1\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{e^{\sin^{-1} x}}{\sqrt{1 - x^{2}}}\)
By the chain rule, with \(u = \sin^{-1} x\):
\( \displaystyle \frac{dy}{dx} = e^{\sin^{-1} x} \cdot \frac{d}{dx}\left(\sin^{-1} x\right) \)
\( \displaystyle = \frac{e^{\sin^{-1} x}}{\sqrt{1 - x^{2}}} \)