If y = a sin3 θ and x = a cos3 θ, then at θ = π/3, dy/dx is equal to
(1) 1/√3 (2) -√3 (3) -1/√3 (4) √3 Solution: y = a sin3 θ Differentiate w.r.t.θ dy/dθ = 3a sin2... View Article
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For 0 < x < 2, (d/dx) ( tan-1 √((1 + cos x/2)/(1 – cos x/2)) is equal to
(1) -1/4 (2) 1/4 (3) -1/2 (4) 1/2 Solution: Let y = ( tan-1 √((1 + cos x/2)/(1 – cos... View Article
If 2x + 2y = 2x+y, then dy/dx is equal to
(1) (2x+ 2y)/(2x– 2y) (2) (2x+ 2y)/(1 + 2x+y) (3) 2x-y(2y -1)/( 1 – 2x ) (4) none of these... View Article
If f(x) and g(x) are two functions with g(x) = x-1/x and fog(x) = x3 -1/x3, then f’(x) is equal to
(1) 3x2 +3 (2) x2– 1/x (3) 1+ 1/x2 (4) 3x2 + 3/x4 Solution: g(x) = x-1/x fog(x) = x3... View Article
If y = f((2x+3)/(3-2x)) and f’(x) = sin (log x), then dy/dx is equal to
(1) sin (log x)/x log x (2) (12/(3-2x)2) [sin log (2x+3)/(3-2x)] (3) cos (log x)/x log x (4) none of... View Article
If [latex]y = \frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}[/latex] , then dy/dx is equal to
(1) ½ cosec2 x/2 (2) ½ cosec x/2 (3) ½ cosec2 x (4) cosec2 x/2 Solution: Given y = (√(1-sin... View Article
Differential coefficient of √(sec√x) is
Differential coefficient of √(sec√x) is (1) (1/4√x) (sec√x) sin √x (2) (1/4√x) (sec√x)3/2 sin √x (3) (½)√x (sec√x) sin √x... View Article
If sec-1 ((1+x)/(1-y)) = a, then dy/dx is equal to
(1) (y-1)/(x+1) (2) (y+1)/(x-1) (3) (x-1)/(y-1) (4) (x-1)/(y+1) Solution: Given sec-1 ((1+x)/(1-y)) = a sec a = (1+x)/(1-y) sec a... View Article
If xy = yx, then x(x-y log x) dy/dx is equal to
1) y (y – x log y) 2) y(y + x log y) 3) x(x + y log x) 4)... View Article
If y = 3at2/(1+t3) and x = 3at/(1+t3), then dy/dx is equal to
(1) t(2-t3)/(1-2t3) (2) t(2+t3)/(1-2t3) (3) t(2-t3)/(1+2t3) (4) t(2+t3)/(1+2t3) Solution: Given y = 3at2/(1+t3) and x = 3at/(1+t3) It is clear... View Article
If sec ((x-y)/(x+y)) = a, then dy/dx is equal to
1) y/x 2) -y/x 3) x/y 4) -x/y Solution: Given sec ((x-y)/(x+y)) = a (x-y)/(x+y) = sec-1 a Differentiate w.r.t.x... View Article
If y = cot-1 (cos 2x)1/2, then the value of dy/dx at x = π/6 will be
1) (2/3)1/2 2) (1/3)1/2 3) (3)1/2 4) (6)1/2 Solution: Given y = cot-1 (cos 2x)1/2 = cot-1 √(cos 2x) dy/dx... View Article
(d/dx)[ xx+ xa +ax + aa ] =
1) xx (1 + log x) + a . xa – 1 2) xx (1 + log x) + a... View Article
[latex]\frac{d}{dx}\left [ \log_{e} e^{\sin x^{2}}\right ][/latex] is equal to
(1) 2 cos x2 (2) 2 cos x (3) 2x cos x (4) 2x cos x2 Solution: Let y =... View Article
If x = A cos 4t + B sin 4t, then d2x/dt2 is equal to
1) -16 x 2) 16 x 3) x 4) -x Solution: x = A cos 4t +B sin 4t Differentiate... View Article
If f(x) = (x – 7)2 (x – 2)7, x ϵ [2, 7]. Then, the value of θ ϵ (2, 7) such that f ‘(θ) = 0 is
1) 49/4 2) 53/9 3) 53/7 4) 49/9 Solution: Given f(x) = (x – 7)2 (x – 2)7 f’(x) =... View Article
If x2 + y2 = t – 1/t and x4 + y4 = t2 + 1/t2, then dy/dx is equal to
(1) 1/x2y2 (2) 1/x2y3 (3) 1/x3y (4) – 1/x3y Solution: Given x2 + y2 = t – 1/t x4 +... View Article
If y = sin[cos–1 {sin (cos–1 x)}], then dy/dx at x = 1/2 equal to
1) 0 2) 1 3) 2/√3 4) 1/√3 Solution: y = sin[cos–1 {sin (cos–1 x)}] = sin[cos–1 {sin (π/2 –... View Article
The derivative of [latex]tan^{-1}left ( frac{sqrt{1+x}-sqrt{1-x}}{sqrt{1+x}+sqrt{1-x}} right )[/latex] is
(1) √(1-x2) (2) 1/√(1-x2) (3) 1/2√(1-x2) (4) x Solution: Let y = tan-1 (√(1+x) – √(1-x) )/(√(1+x) + √(1-x))) Put... View Article
If y = log xx, then the value of dy/dx is
1) xx (1 + log x) 2) log (ex) 3) log (e/x) 4) log (x/e) Solution: Given y = log... View Article
