Question

If \[ y+\sin^{-1}(1-x^2)=e^x, \] then \[ \frac{dy}{dx}= \]

• A. \(e^x-\frac{2}{\sqrt{2-x^2}}\)
• B. \(e^x-\frac{2}{\sqrt{2+x^2}}\)
• C. \(e^x+\frac{2}{\sqrt{2-x^2}}\)
• D. \(e^x+\frac{2}{\sqrt{2+x^2}}\)

Hint:

For \(\sin^{-1}u\), always apply chain rule carefully: derivative is \(\frac{u'}{\sqrt{1-u^2}}\).

Answer 1

The Correct Option is C