Question

Find \(\frac{d^2 y}{dx^2}\), if y=2 sin^-1⁡(cos⁡x).

(a) 0

(b) sin^-1\((\frac{1}{cos⁡x})\)

(c) 1

(d) -1

The question was asked in unit test.

My query is from Second Order Derivatives topic in section Continuity and Differentiability of Mathematics – Class 12

Answer 1

Correct choice is (a) 0

Best explanation: Given that, y=2 sin^-1⁡(cos⁡x)

\(\frac{dy}{dx}=2.\frac{1}{\sqrt{1-cos^2⁡x}}\).-sin⁡x=-2 (∵\(\sqrt{1-cos^2⁡x}\)=sin⁡x)

\(\frac{d^2 y}{dx^2}\)=\(\frac{d}{dx} (\frac{dy}{dx})=\frac{d}{dx}\) (-2)=0