Latest Posts

The derivative of a^{sec x}with respect to a^{tan x} (a > 0) is

1) sec x asec x – tan x 2) sin x a tan x – sec x 3) sin x... View Article

If y = 1 + 1/x + 1/x² + 1/x³ + ….∞ with |x|>1, then dy/dx is equal to

(1) x2/y2 (2) x2y2 (3) y2/x2 (4) -y2/x2 Solution: Given y = 1 + 1/x + 1/x2 + 1/x3 +... View Article

If x = a{cos θ + log tan(θ/2)} and y = a sin θ, then dy/dx is equal to

(1) cot θ (2) tan θ (3) sin θ (4) cos θ Solution: y = a sin θ dy/dθ =... View Article

The value of dy/dx at x = π/2, where y is given by y = x^{sin x} + √x, is

(1) 1 + 1/√(2π) (2) 1 (3) 1/√(2π) (4) 1 – 1/√(2π) Solution: y = xsin x + √x Put... View Article

If f(x + y) = 2f(x) f(y), f ‘(5) = 1024(log 2), f(2) = 8, then the value of f ‘(3) is

Question: If f(x + y) = 2f(x) f(y), f ‘(5) = 1024(log 2), f(2) = 8, then the value of... View Article

If f(x) = (x-1)/4 + (x-1)³/12 + (x-1)⁵/20 + (x-1)⁷/28 +….where 0 < x< 2, then f ‘(x)is equal to

(1) 1/4x(2-x) (2) 1/4(x-2)2 (3) 1/(2-x) (4) 1/(2+x) Solution: f(x) = (x-1)/4 + (x-1)3/12 + (x-1)5/20 + (x-1)7/28 +… f’(x)... View Article

If y = log_a x + log_x a + log_x x + log_a a, then dy/dx is equal to

(1) 1/x + x log a (2) (log a)/x + x/log a (3) x log a (4) 1/x log a... View Article

If y = √((1-x)/(1+x)), then (1-x²)dy/dx + y is equal to

1) 1 2) -1 3) 2 4) 0 Solution: y = √((1-x)/(1+x)) Multiply numerator and denominator with (1-x) y =... View Article

If y = xⁿ log x + x(log x)ⁿ, then dy/dx is equal to

1) xn –1 (1 + n log x) + (log x)n – 1 (n + log x) 2) xn –... View Article

The derivative of f(tan x) with respect to g(sec x) at x = π/4, where f ‘(1) = 2 and g'(√2) = 4, is

1) 1/√2 2) √2 3) 1 4) None of these Solution: Let u = f(tan x), v = g(sec x)... View Article

(d/dx) sin^-1 (x√(1-x) + √x√(1-x²) is equal to

(1) -1/2x√(1-x) – 1/√(1-x2) (2) 1/2√x√(1-x2) – 1/√(1-x2) (3) 1/2√x√(1-x) +1/√(1-x2) (4) -1/2√x√(1-x) +1/√(1-x2) Solution: Let y = sin-1 (x√(1-x)... View Article

If y = log [sin (x²)], 0 < x < π/2, then dy/dx at x = √π/2 is

1) 0 2) 1 3) π/4 4) √π Solution: y = log [sin (x2)] dy/dx = [1/sin (x2)] cos (x2)2x... View Article

The value of differentiation of [latex]e^{x^{2}}[/latex] with respect to e2x–1 at x = 1 is

The value of differentiation of ex2 with respect to e2x–1 at x = 1 is 1) e 2) 0 3)... View Article

If x^y = e^{x – y}, x > 0, then the value of dy/dx at (1, 1) is

1) 0 2) 1/2 3) 1 4) 2 Solution: xy = ex – y y log x = (x-y) log... View Article

If x = cos^-1(1/√(1+t²) and y = sin^-1 (t/√(1+t²)), then dy/dx is equal to

(1) 0 (2) tan t (3) 1 (4) sin t cos t Solution: x = cos-1(1/√(1+t2) Put t = tan... View Article

If x = (1-√y)/(1+√y), then dy/dx is equal to

(1) 4/(x+1)2 (2) 4(x-1)/(x+1)3 (3) (x-1)/(x+1)3 (4) 4/(x+1)3 Solution: x = (1-√y)/(1+√y) Cross multiply x(1+√y) = (1-√y) x+x√y = 1-√y... View Article

If y = cos^–1 (cos x), then dy/dx is

1) 1 in the whole plane 2) –1 in the whole plane 3) 1 in the 2nd and 3 rd... View Article

If f ‘(x) = g(x) and g'(x) = – f(x) for all x and f(2) = 4 = f ‘(2), then f ² (4) + g²(4) is equal to

1) 8 2) 16 3) 32 4) 64 Solution: Let h(x) = f(x)2 + g(x)2 Differentiate with respect to x... View Article

If y = tan^-1 √((1-sin x)/(1+sin x)), then the value of dy/dx at x = π/6 is

(1) 1/2 (2) -1/2 (3) 1 (4) -1 Solution: y = tan-1 √((1-sin x)/(1+sin x)) = tan-1 √((1-cos ((π/2)-x)/(1+cos ((π/2)-x))... View Article

The derivative of tan^-1 (2x/1-x²) with respect to cos^-1 √(1-x²) is

(1) √(1-x2)/(1+x2) (2) 1/√(1-x2) (3) 2/(1+x2) (4) 2√(1-x2)/(1+x2) Solution: Let u = tan-1 (2x/1-x2) Put x = tan θ u... View Article

«
1
…
3,498
3,499
3,500
3,501
3,502
…
5,472
»