Find the derivative of cos⁻¹(sin x) with respect to x, for x in (0, π/2). A. 1 B. −1 C. 0 D. cos x Answer: B) −1 Explanation: We can write sin x as cos(π/2 − x). So, cos⁻¹(cos(π/2 − x)) = π/2 − x. The derivative of π/2 − x is −1.

imo class 12 continuity and differentiability

Find the derivative of cos⁻¹(sin x) with respect to x, for x in (0, π/2).

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Find the derivative of cos⁻¹(sin x) with respect to x, for x in (0, π/2).

Answer: B) −1

Explanation: We can write sin x as cos(π/2 − x). So, cos⁻¹(cos(π/2 − x)) = π/2 − x. The derivative of π/2 − x is −1.