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 y = e Differentiate w.r.t.x cos y dy/dx + e-x cos y... 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 y = cosh-1 (sec x) dy/dx =... 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 = ex log x Use product rule dy/dx = ex log x +... 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)) = [1/f(ex+ 2x)] × f’(ex+ 2x) (ex + 2) = (ex... 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 w.r.t.x f’(x) = -1/√(1-[ (1... 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 = e√x×(1/2√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)[ 1/√(x2+a2) + 1/√(x2+b2) ] (4) (a2... 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) = lim h→ 0[ f(c+h) - f(c)]/h Here c = -3... 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, if x>0 f’(x) = -2x, if x<0 f’(x)... 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 Solution: Let y = sin 2x2 Differentiate w.r.t.x dy/dx =... 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 dp/dv = -81/v2 Put v = 9 dp/dv =... 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 = (1 - x)/x2 = 1/x2 - 1/x Differentiate... View Article
The value of x at which the first derivative of the function (√x + 1/√x)2 w.r.t.x is 3/4 are (1) ±2 (2) ±1/2 (3) ±2/√3 (4) ±√3/2 Solution: Given f(x) = (√x + 1/√x)2 = x + 1/x + 2 Differentiate w.r.t.x f’(x) = 1 - 1/x2... View Article
The first derivative of the function sin 2x cos 2x cos 3x + log2 2x+3 with respect to x at x = π is (1) 2 (2) -1 (3) 1 (4) none of these Solution: Given f(x) = sin 2x cos 2x cos 3x + log2 2x+3 = (½) sin 4x cos 3x + (x+3) log2 2... View Article
Derivative of the function f(x) = log5(log7 x), x> 7 is (1) 1/x log 5 log 7 log7 x (2) 1/x log 5 log 7 (3) 1/x log x (4) none of these Solution: We know logba = log a/log b f(x) =... View Article
If y = cot-1 x2, then dy/dx is equal to (1) 2x/(1 + x4) (2) 2x/√(1 + 4x) (3) -2x/(1 + x4) (4) -2x/√(1 + x2) Solution: Given y = cot-1 x2 Differentiate w.r.t.x dy/dx =... View Article
If y = log tan √x, then the value of dy/dx is (1) 1/2√x (2) sec2√x/(√x tan √x) (3) 2sec2√x (4) sec2√x/(2√x tan √x) Solution: Given y = log tan √x Differentiate w.r.t.x dy/dx... View Article
If y = sec xo, then dy/dx = (1) sec x tan x (2) sec xo tan xo (3) (π/180) sec xo tan xo (4) (180/π) sec xo tan xo Solution: Given y = sec xo We know π... View Article
If [latex]y = \cot^{-1}\left [ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \right ][/latex], then dy/dx = (1) 1/2 (2) 2/3 (3) 3 (4) 1 Solution: Given y = cot-1 [ √(1 + sin x) + √(1 - sin x)]/[√(1 + sin x) - √(1 - sin x)] Multiply... View Article
