1) For xϵ(0,14), if the derivative of tan−1(6x√x1−9x3) is √x .g(x), then g(x) equals A) 91+9x3 B) 3x√x1−9x3 C) 3x1−9x3 D) 31−9x3 Answer: Option AExplanation:Let y= tan−1(6x√x1−9x3) = tan−1(2.(3x32)1−(3x32)2] = 2tan−1(3x32) [∵2tan−1x=tan−12x1−x2] ∴dydx=2.11+(3x32)2.3×32x12 = 91+9x3.√x g(x) = 91+9x3