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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Differentiate the cos–1 (sin x) w.r.t. x.
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Answer

Let f (x) = cos–1 (sin x). Observe that this function is defined for all real numbers. We may rewrite this function as
f(x) = cos–1 (sin x)}
= cos-1$\left[\cos \left(\frac{\pi}{2}-x\right)\right]$
= $\frac{\pi}{2}-x$
Thus f ′(x) = –1.

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