Question

Find the value f′(x), if f(x)=sin−1⁡(1−x2)

• A. (A) 11−x2
• B. (B) 22−x2
• C. (C) −22−x2
• D. (D) −11−x2

Answer 1

Answer: (C)

(C) −22−x2

Answer 2

Explanation:
Concept:ddxsin−1⁡x=11−x2ddxtan−1⁡x=11+x2Let u=1−x2dudx=−2xy=sin−1⁡(1−x2)=sin−1⁡udydx=dydu×dudxdydx=ddusin−1⁡u×(−2x)dydx=11−u2×(−2x)dydx=−2x1−(1−x2)2dydx=−2x2x2−x4dydx=−22−x2Hence, the correct option is (C).