Q44 of 354 Page 12

If y = cos–1 (2x) + 2 cos–1 < x < 0, find .


Put 2x = cos θ



y = cos–1(cosθ) + 2cos–1(sinθ )



Considering the limits



–1 < 2x < 0


–1 < cosθ < 0





Now,





y = –π + cos–1(2x)


Differentiating w.r.t x we get





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