For the curve √x + √y = 1, dy/dx at (¼, ¼) is
(1) 1 (2) ½ (3) -1 (4) 2 Solution: Given √x + √y = 1 Differentiate w.r.t.x 1/2√x + (1/2√y)dy/dx... View Article
Latest Posts
If y = (cos x2)2, then dy/dx is equal to
(1) -4x sin 2x2 (2) -x sin x2 (3) -2x sin 2x2 (4) -x cos 2x2 Solution: Given y =... View Article
If y = (x+1)(x+2)(x+3)(x+4)(x+5), then the value of dy/dx at x = 0 is equal to
(1) 742 (2) 472 (3) 374 (4) 274 Solution: Given y = (x+1)(x+2)(x+3)(x+4)(x+5) Differentiate w.r.t.x dy/dx = (x+2)(x+3)(x+4)(x+5) + (x+1)(x+3)(x+4)(x+5)... View Article
If [latex]f(x)= 3e^{x^{2}}[/latex], then f’(x) – 2xf(x) + ⅓ f(0) – f’(0) =
(1) 1 (2) 0 (3) 7/3 (4) none of these Solution: Given \(\begin{array}{l}f(x)= 3e^{x^{2}}\end{array} \) \(\begin{array}{l}f'(x)= 3e^{x^{2}}2x\end{array} \) \(\begin{array}{l}= 6xe^{x^{2}}\end{array}... View Article
If y = xn log x + x(log x)n, then dy/dx =
(1) xn-1( 1 + n log x ) + (log x)n-1 (n + log x) (2) xn-2( 1 + n... View Article
The derivative of tan x – x with respect to x is
(1) 1-tan2x (2) tan x (3) -tan2x (4) tan2x Solution: Let y = tan x – x Differentiate w.r.t.x dy/dx... View Article
If y = sin-1√(1-x) + cos-1 √x, then dy/dx =
(1) 1/√(x(1-x)) (2) -1/√(x(1-x)) (3) 1/√(x(1+x)) (4) none of these Solution: Given y = sin-1√(1-x) + cos-1 √x dy/dx =... View Article
If y = sin-1 √x, then dy/dx =
(1) 2/√x√(1 – x) (2) -2/√x√(1 – x) (3) 1/2√x√(1 – x) (4) 1/√(1 – x) Solution: Given y =... View Article
d/dx [ log (x + 1/x)] =
(1) x + 1/x (2) (1 + 1/x2)/(x + 1/x) (3) (1 – 1/x2)/(x + 1/x) (4) 1 + 1/x... View Article
d/dx[tan-1 (a+x)/(1-ax)] = …; a is constant, a,x∈R+; ax<1
(1) a/(1+x2) (2) -a(1+x2) (3) 1/(1+x2) (4) -1/(1+x2) Solution: Let y = tan-1 (a+x)/(1-ax) = tan-1 a + tan-1 x... View Article
If y = sin-1x/√(1-x2), then (1-x2)dy/dx is equal to
(1) x+y (2) 1+xy (3) 1-xy (4) xy-2 Solution: y = sin-1x/√(1-x2) y√(1-x2) = sin-1x Differentiate w.r.t.x (dy/dx)√(1-x2) + y×1/2√(1-x2)... View Article
If y = sin-1 [(5x+12√(1-x2))/13], then dy/dx is equal to
(1) 1/√(1-x2) (2) -1/√(1-x2) (3) 3/√(1-x2) (4) x/√(1-x2) Solution: Given y = sin-1 [(5x+12√(1-x2))/13] Put x = sin θ θ... View Article
[latex]\frac{d}{dx}e^{x^{3}}[/latex] is equal to
(1) \(\begin{array}{l}3xe^{x^{3}}\end{array} \) (2) \(\begin{array}{l}3x^{2}e^{x^{3}}\end{array} \) (3) \(\begin{array}{l}3xe^{x^{2}}\end{array} \) (4) \(\begin{array}{l}2x^{2}e^{x^{2}}\end{array} \) Solution: Given y = \(\begin{array}{l}e^{x^{3}}\end{array} \) Differentiate w.r.t.x... View Article
If y = logsin x tan x, then dy/dx at π/4 is equal to
(1) 4/log 2 (2) -4 log 2 (3) -4 /log 2 (4) none of these Solution: Given y = logsin... View Article
If y = (1+x1/4) (1+x1/2)(1-x1/4), then dy/dx =
(1) 1 (2) -1 (3) x (4) √x Solution: Given y = (1 + x1/4) (1 + x1/2)(1 – x1/4)... View Article
If y = log log x, then ey dy/dx =
(1) 1/x (2) 1/x log x (3) 1/log x (4) ey Solution: Given y = log log x dy/dx =... View Article
d/dx [ eax cos (bx+c)] =
(1) eax (a cos (bx+c) – b sin (bx+c)) (2) eax (a cos (bx+c) + b sin (bx+c)) (3) eax... View Article
Let f(x) be a polynomial function of the second degree. If f(1) = f(-1) and a1, a2, a3 are in AP, then f’(a1), f’(a2), f’(a3) are in
(1) AP (2) GP (3) HP (4) none of these Solution: Let f(x) = px2 + qx + r f(1)... View Article
d/dx [log √(sin √ex)] =
(1) (¼) ex/2 cot ex/2 (2) ex/2 cot ex/2 (3) (¼) ex cot ex (4) (½) ex/2 cot ex/2 Solution:... View Article
[latex]frac{d}{dx}left ( log left ( frac{e^{x}}{1+e^{x}} right ) right )=[/latex]
(1) 1/(1-ex) (2) -1/(1+ex) (3) -1/(1-ex) (4) none of these Solution: Let y = log (ex)/(1+ex) Differentiate w.r.t.x dy/dx =... View Article
