tan-1 (√3) – cot-1 (-√3) is equal to
1) 0 2) 2√3 3) – (π / 2) 4) π Solution: (3) – (π / 2) tan-1 (√3) –... View Article
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If we consider only the principle values of the inverse trigonometric functions then the value of tan [cos-1 (1 / 5√2) – sin-1 (4 / √17)] is
1) √29 / 3 2) 29 / 3 3) √3 / 29 4) 3 / 29 Solution: (4) 3 /... View Article
Given that d/dx f(x) = f’(x). The relationship f’(a+b) = f’(a) + f’(b) is valid if f(x) is equal to
(1) x (2) x2 (3) x3 (4) x4 Solution: Check the options and verify the condition. Let f(x) = x2... View Article
If f(x) = √(ax) + a2/√(ax), then f’(a) =
(1) -1 (2) 0 (3) 1 (4) a Solution: Given f(x) = √(ax) + a2/√(ax) Differentiate w.r.t.x f’(x) = [√a/2√x)]... View Article
10-x tan x [d/dx 10x tan x ] is equal to
(1) tan x – x sec2 x (2) log 10 [ tan x + x sec2 x] (3) x tan... View Article
If y = cot-1 tan (x/2), then dy/dx is equal to
(1) 0 (2) ½ (3) -½ (4) x/2 Solution: We know d/dx cot-1x = -1/(1 + x2) d/dx cot-1 tan... View Article
[latex]\frac{d}{dx}\left [ \left ( \frac{\tan ^{2}2x-\tan ^{2}x}{1-\tan ^{2}2x\tan ^{2}x} \right ) \cot 3x\right ][/latex]
(1) sec2 x (2) sec x tan x (3) tan 2x tan x (4) none of these Solution: Let y... View Article
If sin y + e-x cos y = e, then dy/dx at (1, π) is
(1) e (2) sin y (3) cos y (4) sin y cos y Solution: Given sin y + e-x cos... View Article
d/dx cosh-1 (sec x) =
(1) sec x (2) tan x (3) sin x (4) cosec x Solution: We know d/dx cosh-1x = 1/√(x2-1) Let... View Article
If y = ex log x, then dy/dx is
(1) ex/x (2) ex (log x + 1/x) (3) ex (x log x + 1/x) (4) ex/log x Solution: y... View Article
If f(1) = 3, f’(1) = 2, then d/dx( log f(ex+ 2x)) at x = 0 is equal to
(1) 0 (2) 2 (3) 3/2 (4) 2/3 Solution: Given f(1) = 3 f’(1) = 2 d/dx( log f(ex+ 2x))... View Article
If f(x) = cos-1[ (1 – (log x)2)/(1 + (log x)2)], then the value of f’(e)
(1) 1 (2) 1/e (3) 2/e (4) 2/e2 Solution: f(x) = cos-1[ (1 – (log x)2)/(1 + (log x)2)] Differentiate... View Article
If y = e√x, then dy/dx equals
(1) e√x/2√x (2) √x/e√x (3) x/e√x (4) 2√x/e√x Solution: Given y = e√x Differentiate w.r.t.x dy/dx = e√x× d/dx √x... View Article
The derivative of √(√x+1) is
(1) 1/√x √(√x+1) (2) 1/√x (√x+1) (3) 4/√x √(√x+1) (4) 1/4 √(x√x+1) Solution: Let y = √(√x+1) Differentiate w.r.t.x dy/dx... View Article
If [latex]f(x)=\frac{1}{\sqrt{x^{2}+a^{2}}+\sqrt{x^{2}+b^{2}}}[/latex], then f’(x) is equal to
(1) x/(a2 – b2)[ 1/√(x2+a2) – 1/√(x2+b2) ] (2) x/(a2 – b2)[ 1/√(x2+a2) – 2/√(x2+b2) ] (3) x/(a2 – b2)[... View Article
The derivative of f(x) = 3|2 + x| at the point x0 = -3 is
(1) 3 (2) -3 (3) 0 (4) does not exist Solution: Given f(x) = 3|2 + x| We know f’(c)... View Article
The derivative of f(x) = x|x| is
(1) 2x (2) -2x (3) 2x2 (4) 2|x| Solution: f(x) = x|x| f(x) = -x2, if x<0 f(x) = x2,... View Article
d/dx (sin 2x2) equals
(1) 4x cos 2x2 (2) 2 sin x2 cos x2 (3) 4x sin x2 (4) 4x sin x2 cos x2... View Article
If pv = 81, then dp/dv at v = 9 is equal to
(1) 1 (2) -1 (3) 2 (4) none of these Solution: Given pv = 81 p = 81/v Differentiate w.r.t.v... View Article
If y = (1 – x)/x2, then dy/dx is
(1) 2/x2 + 2/x3 (2) -2/x3 + 1/x2 (3) -2/x2 + 2/x2 (4) none of these Solution: Given y =... View Article
