# CBSE Guess paper class XII Mathematics 2008 5

EGuess Paper – 2008

Class – XII

Subject – Mathematics

DIFFERENTIATION

 1 x2 sin xy + y cos x = 2 2 (x2 + 2y)2 + x3 + y2 = 2x 3 tan-1 _3x – 4_ 1 + 12x 4 tan-1 √(1 + a2x2) – 1 ax 5 cos-1 3 + 5cosx 5+3cos x 6 cos-1 1 – x2p 1 + x2p 7 x2 sin3 x cos4 x 8 log sinm x cosn x 9 log tan x – cot x log (1+sin x) 2 10 __sin2x__ + __cos2x__ 1 + cot x 1 + tan x 11 If y = √x + 1/x, show that 2x dy/dx + y = 2√x 12 If y = 1 + x + x2 + x3 +…+ xn 2! 3! n! show that, dy + xn = y dx n! 13 If y = log 1 + tan x 1/2 1 – tan x prove that dy/dx = sec 2x 14 If yx + xy = K, show that dy = - yx log y + yxy – 1 dx xy log x + xyx – 1 15 If x + y = sin (x + y), show that dy/dx = - 1 16 If ex+ y = xy, show that dy/dx = y (1 – x)/x ( y – 1) 17 If √(1–x4) + √(1–y4) = k (x2– y2) s.t. y√(1–x4) dy/dx = x √(1–y4) 18 If y= tan-1xn+tannx – tan-1 a+xn 1-axn s.t.dy/dx = n tann-1x sec2x 19 If x = a(cos θ + θ sin θ) and y = a(sin θ – θ cos θ), show that, a θ d2y/dx2 = sec3 θ 20 If y = sin-1 x/ √(1–x2), show that, (1–x2)d2y/dx2 –3x dy/dx–y =0