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If y = x^{x^x^….. ∞}, then dy / dx =

1) y2 / [x (1 + y log x)] 2) y2 / [x (1 – y log x)] 3) y... View Article

1) (x2 + 4) (dy / dx)2 = n2 (y2 + 4) 2) (x2 + 4) (dy / dx)2 =... View Article

1) {[6x2 – 2x + 2] / (x2 + 1)2} sin [(2x – 1)2 / (x2 + 1)] 2) {[6x2... View Article

1) 0 2) –1 3) 1 4) 2 Solution: (3) 1 ux = (y / x) + log y uy... View Article

1) –1 2) –2 3) 1 4) 2 Solution: (3) 1 xexy = y + sin2 x At x =... View Article

1) a = b and c ≠ b 2) a = c and a ≠ b 3) a ≠ b... View Article

1) (2 / 3)1/2 2) (1 / 3)1/2 3) (3)1/2 4) (6)1/2 Solution: (1) (2 / 3)1/2 y = cot-1... View Article

1) √x2 + a2 2) 1 / [√x2 + a2] 3) 2√x2 + a2 4) 2 / √x2 + a2... View Article

1) –1 2) –0.5 3) 0.5 4) 1 Solution: (3) 0.5 f (x) = x3 f (x + h) =... View Article

1) f (x) = |x| in – 2 ≤ x ≤ 2 2) f (x) = tan x in 0 ≤ x... View Article

1) 3 / 4 2) 4 / 3 3) 1 / 3 4) 2 / 3 5) 5 / 3... View Article

1) f (x) = x 2) f (x) = x2 3) f (x) = 2x3 + 3 4) f (x)... View Article

1) 2 2) –2 3) 1 4) –1 Solution: Given sin(x + y) = log(x + y) Differentiate w.r.t.x, we... View Article

If f(x) = x/(1 + x) and g(x) = f[f(x)], then g'(x) is equal to (1) 1/(2x+3)2 (2) 1/(x+1)2 (3)... View Article

1) 4 2) 3 3) –4 4) –3 Solution: Given f(x) = x2 + bx + 7 f’(x) = 2x... View Article

(1) P’’’(x) + P’(x) (2) P’’(x) P’’’(x) (3) P(x) P’’’(x) (4) a constant Solution: Given y2 = P(x) Differentiate w.r.t.x,... View Article

1) 1 + x5 2) 5x4 3) 1/(1 + {g(x)}5) 4) 1 + {g(x)}5 Solution: Given g is the inverse... View Article

(1) cot z (2) 2 cot z (3) 2 tan z (4) 2 sec z Solution: Given z = sec-1... View Article

(1) -1 (2) 0 (3) 2 (4) 1 Solution: f(x,y) = cos (x-4y)/cos (x+4y) ∂f/∂x = [ – cos (x+4y)... View Article

(1) 0 (2) 1 (3) 2 (4) none of these Solution: u = sin-1 (x/y) + tan-1(y/x) = sin-1 (1/(y/x))... View Article