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[latex]\frac{d}{dx}xe^{x^{2}}=[/latex]

(1) \(\begin{array}{l}\ 2x^{2}e^{x^{2}}\end{array} \) (2) \(\begin{array}{l}\ e^{x^{2}}+2x^{2}e^{x^{2}}\end{array} \) (3) \(\begin{array}{l}\ x^{2}e^{x^{2}}+e^{x^{2}}\end{array} \) (4) none of these Solution: Let \(\begin{array}{l}y =... View Article

[latex]\frac{d}{dx}\log (\sec x+\tan x)=[/latex]

(1) cosec x (2) sec x (3) tan x (4) cos x Solution: Let y = (log (sec x +... View Article

[latex]\frac{d}{dx}\left ( e^{x\sin x} \right )=[/latex]

(1) ex sin x (x cos x + sin x) (2) ex sin x ( cos x + x sin... View Article

[latex]\frac{d}{dx}\left [ \tan^{-1}\sqrt{\frac{1-\cos x}{1+\cos x}} \right ]=[/latex]

(1) ½ (2) 0 (3) 1 (4) -½ Solution: Let y = [ tan-1 √((1-cos x)/(1 + cos x)] =... View Article

[latex]\frac{d}{dx}\left [ \log \sqrt{\frac{1-\cos x}{1+\cos x}} \right ]=[/latex]

(1) cosec x (2) sec x (3) cosec x/2 (4) sec x/2 Solution: Let y = [ log √((1 –... View Article

The differential coefficient of the given function [latex]log_{e}left ( sqrt{frac{1+sin x}{1-sin x}} right )[/latex] is

(1) cosec x (2) sec x (3) tan x (4) cos x Solution: Let y = loge (√((1 + sin... View Article

If [latex]y = \cot^{-1}\left ( \frac{1+x}{1-x} \right )[/latex], then dy/dx =

(1) 1/(1+x2) (2) -1/(1+x2) (3) 2/(1+x2) (4) -2/(1+x2) Solution: Given y = cot-1 (1+x)/(1-x) Put x = tan θ θ... View Article

If [latex]y = \tan^{-1}\left ( \frac{x^{\frac{1}{3}}+a^{\frac{1}{3}}}{1-x^{\frac{1}{3}}a^{\frac{1}{3}}} \right )[/latex], then dy/dx =

(1) 1/3x2/3(1+x2/3) (2) a/3x2/3(1+x2/3) (3) -1/3x2/3(1+x2/3) (4) -a/3x2/3(1+x2/3) Solution: Given y = tan-1 (x1/3 + a1/3)/(1 -x1/3a1/3) = tan-1 x1/3... View Article

[latex]\frac{d}{dx}\left ( x^{3} \tan ^{2}\frac{x}{2}\right )=[/latex]

(1) x3 tan (x/2) sec2(x/2) + 3x tan2(x/2) (2) x3 tan2 (x/2) sec2(x/2) + 3x2 tan2(x/2) (3) x3 tan (x/2)... View Article

[latex]\frac{d}{dx}\left ( \frac{\sec x+\tan x}{\sec x-\tan x} \right )=[/latex]

(1) 2 cos x/(1-sin x)2 (2) cos x/(1-sin x)2 (3) 2 cos x/(1-sin x) (4) none of these Solution: Let... View Article

[latex]\frac{d}{dx}\sqrt{\sec ^{2}x+cosec^{2}\: x}=[/latex]

(1) 4 cosec 2x cot 2x (2) -4 cosec 2x cot 2x (3) 4 cosec x cot 2x (4) none... View Article

[latex]\frac{d}{dx}\sqrt{x\sin x}=[/latex]

(1) (sin x + x cos x )/2√(x sin x) (2) (sin x + x cos x )/√(x sin x)... View Article

[latex]\frac{d}{dx}\left ( x^{2} +\cos x\right )^{4}=[/latex]

(1) 4(x2 + cos x )(2x – sin x) (2) 4(x2 – cos x )3(2x – sin x) (3) 4(x2... View Article

If [latex]y = \left ( \frac{1+\tan x}{1-\tan x} \right )[/latex], then dy/dx =

(1) sec2x/(1-tan x)2 (2) 2 sec2x/(1-tan x)2 (3) 2 sec2x/(1+tan x)2 (4) none of these Solution: Given y = (1+tan... View Article

If [latex]y = \sin \left ( \frac{1+x^{2}}{1-x^{2}} \right )[/latex] , then dy/dx =

(1) (4x/(1-x2) ) cos ((1+x2)/(1-x2)) (2) (x/(1-x2) ) cos ((1+x2)/(1-x2)) (3) (4x/(1-x2)2 ) cos ((1+x2)/(1-x2)) (4) (x/(1-x2)2 ) cos ((1+x2)/(1-x2))... View Article

If y = sin (√(sin x + cos x)), then dy/dx =

(1) (1/2) cos (√(sin x + cos x)) ( cos x – sin x)/√(sin x + cos x) (2) (1/2)... View Article

If y = (x cot³ x)^3/2, then dy/dx =

(1) (3/2)(x cot3 x)1/2 [ cot3x – 3x cot2x cosec2x ] (2) (3/2)(x cot3 x)1/2 [ cot2x – 3x cot2x... View Article

If y = [√(a+x) – √(a-x)]/[√(a+x) +√(a-x)], then dy/dx =

(1) ay/x√(a2-x2) (2) ay/√(a2-x2) (3) ay/x√(x2-a2) (4) none of these Solution: Given y = [√(a+x) – √(a-x)]/[√(a+x) +√(a-x)] Multiply numerator... View Article

If A = (2^x cot x)/√x, then dA/dx =

(1) (2x/√x) [ log 2 cot x – cosec2 x – (cot x)/2x ] (2) (2x/x) [ log 2 cot... View Article

If y = (tan x + cot x)/(tan x – cot x), then dy/dx =

(1) 2 tan 2x sec 2x (2) tan 2x sec 2x (3) -tan 2x sec 2x (4) -2 tan 2x... View Article

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