Choose the correct alternative in the following:
The derivative of cos–1 (2x2 – 1) with respect to cos–1 x is
Let u = cos–1 (2x2 – 1) and v = cos–1 x
Considering u = cos–1 (2x2 – 1)
Put x = cos θ ⇒ θ = cos-1x ---(1)
u = cos–1 (2cos2θ – 1)
u = cos–1 (cos2θ) ∵ 2cos2θ – 1 = cos2θ
u = 2θ
u = 2 cos-1x -- From(1)
Differentiating w.r.t x we get,
Considering v = cos–1 x
Differentiating w.r.t x we get,
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