The derivative of cos-1(2x2 – 1) w.r.t. cos-1 x is

Let u = cos-1(2x2 – 1) and v = cos-1 x


Now, u = cos-1(2x2 – 1)


= cos-1(2cos2v – 1) [∵v = cos-1 x ⇒ cos v = x]


= cos-1(cos2v) [∵ 2cos2x – 1 = cos2x]


⇒ u = 2v


⇒

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