If Y X X2 Then The Derivatives Of Y2 With Respect To X2 Is 1) 2x2 + 3x – 1 2) 2x2 – 3x + 1 3) 2x2 + 3x + 1 4) 2x2 – 3x – 1 Solution: y = x - x2 Squaring both sides y2 = (x-x2)2 y2 =... View Article
If Y Be An Implicit Function Of X Defined By X 2x 2x X Cot Y 1 0 Then Y 1 Is Equal To 1) –1 2) 1 3) log 2 4) – log 2 Solution: Given x2x – 2xx cot y – 1 = 0 Let u = x2x log u = 2x log x Differentiate w.r.t.x... View Article
If Y 1 X 1 X2 1 X4 1 X 2n Then The Value Of Dy Dx At X 0 Is 1) 0 2) -1 3) 1 4) 2 Solution: y = (1 + x) (1 + x2) (1 + x4)...(1 + x2n) Use product rule dy/dx = 1(1 + x2) (1 + x4)...(1 + x2n)... View Article
If Xy E2 X Y Then Dy Dx Is Equal To (1) 2(1+log x)/(2+log x)2 (2) (1+log x)/(2+log x)2 (3) 2/(2+log x) (4) 2(1-log x)/(2+log x)2 Solution: xy = e2(x – y) Taking... View Article
If Fx Mod X 2 X 1 X Then F 10 Is Equal To 1) –3 2) –2 3) –1 4) 0 Solution: f(x) = |x - 2| + |x + 1|- x (d/dx)|x| = |x|/x or x/|x| f’(x) = [|x - 2|/(x-2)] + [|x + 1|/(x... View Article
If Y Sin X Sin 2x Sin 3x Sin Nx Then Dy Is 1) 2) 3) 4) Solution: y = sin x . sin 2x . sin 3x... sin nx Take log log y = log (sin x . sin 2x . sin 3x... sin nx)... View Article
If Pi Less Than X Less Than 2 Pi Then D Dx Tan 1 1 Cos X 1 Cos X 2 Is (1) 0 (2) 1 (3) 1/2 (4) -1/2 Solution: (d/dx) [ tan-1((1-cos x)/(1+cos x))1/2] = (d/dx)((2 sin2x)/2)1/2/((2 cos2x)/2)½ (π < x... View Article
D Dx Sin 1 X A Eq A Less Than 0 And Mod X A Less Than 1 (1) 1/√(a2-x2) (2) 1/√(x2-a2) (3) -1/√(a2-x2) (4) -1/√(x2-a2) Solution: Hence option (1) is the answer.... View Article
If Fx Int Log T Dt X2 And X3 X 0 Then F X Is Equal To 1) (9x2 – 4x)log x 2) (4x – 9x2) log x 3) (9x2 + 4x)log x 4) (3x2 – 2x)log x Solution: ∫ log t dt = t log t - t +c Apply upper... View Article
If Fx Loge Loge X Then F E Is Equal To 1) e-1 2) e 3) 1 4) 0 Solution: f(x) = loge (loge x) f’(x) = (1/loge x)(1/x) Put x = e f’(e) = (1/loge e)(1/e) = 1/e (since... View Article
If Y 3x 1 3x 1 Sin X Loge 1 X X 1 Then At X 0 Dy Dx Is Equal To 1) 1 2) 0 3) -1 4) -2 Solution: y = [(3x-1)/(3x+1)]sin x + loge (1+x) dy/dx = [(3x log 3 (3x+1) - (3x-1)3x log 3)/(3x+1)2)] sin x... View Article
If Pi 2 Less Than X Less Than 3pi 2 Then The Value Of D Dx Tan 1 Cos X 1 Sin X Is Equal To 1) 1/2 2) -1/2 3) 1 4) -1 Solution: = -½ Hence option (2) is the answer.... View Article
If The Function Fx Defined By Fx X100 100 X99 99 X2 2 X 1 Then F0 Is Equal To 1) 100 f’(0) 2) 100 3) 1 4) -1 Solution: f(x) = x100/100 + x99/99 + …+x2/2 + x + 1 f’(x) = x99 + x98 + ….x + 1 Put x = 0 f’(0)... View Article
If Ex Ey Ex Y Then Dy Dx At 2 2 Is 1) 1 2) –1 3) 2 4) None of these Solution: ex + ey = ex + y Differentiating both sides w.r.t.x ex + ey(dy/dx) = ex +... View Article
If Fx Logx Lnx Then Fe Is Equal To 1) 1/e 2) e 3) –e 4) e2 Solution: f(x) = logx {ln(x)} = logx log(x) = log (log x)/log x Apply quotient rule of differentiation... View Article
The Derivative Of Y 1 X 2 X N X At X 1 Is 1) 0 2) (–1)(n – 1)! 3) n! – 1 4) (–1)n–1 (n – 1)! Solution: y = (1 - x) (2 - x) ...(n - x) Use product rule dy/dx = -1(2 -... View Article
Find The Derivative Of Root 2x 2 Root X 1 Root X (1) √2 + (1/√x)(1 - 1/2x) (2) √2 - (1/√x)(1+ 1/2x) (3) √2 - (1/√x)(1 - 1/2x) (4) √2 + (1/√x)(1+ 1/2x) Solution: y = √2x + 2√x -... View Article
If Y F X2 2 And F3 5 Then Dy Dx At X 1 Is 1) 5 2) 25 3) 15 4) 10 Solution: Given f '(3) = 5 y = f(x2 + 2) dy/dx = f’(x2 + 2) 2x Put x = 1 dy/dx = f’(1 + 2)2 = f '(3)×... View Article
If Y 1 X 1 X2 1 X4 Then Dy Dx At X 1 Is (1) 20 (2) 28 (3) 1 (4) 0 Solution: y = (1 + x) (1 + x2) (1 + x4) Apply product rule y’ = (1 + x2) (1 + x4) + 2x (1 + x)(1 + x4)... View Article
The Equation Of The Tangent To The Curve Y X 4 X 2 That Is Parallel To The X Axis Is 1) y = 0 2) y = 1 3) y = 2 4) y = 3 Solution: (4) y = 3 Slope of the line parallel to x-axis = 0 y = x + [4 / x2] y’ = 1 + (-2)... View Article