The derivative of [latex]sin^{-1}left ( frac{2x}{1+x^{2}} right )[/latex] w.r.t [latex]cos^{-1}left ( frac{1-x^{2}}{1+x^{2}} right )[/latex] is
(1) 1 (2) 2 (3) -1 (4) 4 Solution: Let u = sin-1 2x/(1 + x2) v = cos-1 ((1... View Article
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If [latex]u=\tan^{-1}\left ( \frac{\sqrt{1+x^{2}}-1}{x} \right )[/latex] and [latex]v=\tan^{-1}x[/latex], then du/dv is equal to
(1) 4 (2) 1 (3) 1/4 (4) -1/4 Solution: Given u = tan-1 (√(1+x2)-1)/x Put x = tan θ u... View Article
The differential coefficient of [latex]tan^{-1}sqrt{frac{1-x^{2}}{1+x^{2}}}[/latex] with respect to [latex]cos^{-1}x^{2}[/latex] is
(1) 1/2 (2) -1/2 (3) 1 (4) 0 Solution: Let u = tan-1 √((1 – x2)/(1 + x2)) Put x2... View Article
The differential coefficient of x6 with respect to x3 is
(1) 5x2 (2) 3x3 (3) 5x3 (4) 2x3 Solution: Let u = x6 Differentiate w.r.t.x du/dx = 6x5 Let v... View Article
The differential coefficient of tan-1 √x with respect to √x is
(1) 1/(1 + x) (2) 1/2x√(1 + x) (3) 1/2√x(1 + x) (4) none of these Solution: Let u =... View Article
The differential coefficient of [latex]tan^{-1}left ( frac{sqrt{1+x^{2}}-1}{x} right )[/latex] with respect to [latex]tan^{-1}x[/latex]
(1) 1/2 (2) -1/2 (3) 1 (4) none of these Solution: Let u = tan-1 (√(1+x2)-1)/x Put x = tan... View Article
Differential coefficient of [latex]frac{tan^{-1}x}{1+tan^{-1}x}[/latex] w.r.t.[latex]tan^{-1}x[/latex] is
(1) 1/(1 + tan-1 x) (2) -1/(1 + tan-1 x) (3) 1/(1 + tan-1 x)2 (4) -1/2(1 + tan-1 x)2... View Article
The differential coefficient of [latex]tan^{-1}left ( frac{2x}{1-x^{2}} right )[/latex] w.r.t [latex]sin^{-1}left ( frac{2x}{1+x^{2}} right )[/latex] is
(1) 1 (2) -1 (3) 0 (4) none of these Solution: Let u = tan-1 2x/(1 – x2) Put x... View Article
Differential coefficient of sin-1 x w.r.t.cos-1 √(1 – x2) is
(1) 1 (2) 2 (3) 1/(1 + x2) (4) none of these Solution: Let u = sin-1 x Differentiate w.r.t.x... View Article
Differential coefficient of sin-1 (1 – x)/(1 + x) w.r.t. √x is
(1) 1/2√x (2) √x/√(1-x) (3) 1 (4) -2/(1+x) Solution: Let u = sin-1(1 – x)/(1 + x) v = √x... View Article
[latex]\frac{d}{dx}\left ( \tan^{-1}\frac{\sqrt{1+x^{2}}-1}{x} \right )[/latex]
(1) 1/(1 + x2) (2) 1/2(1 + x2) (3) -2/(1 + x2) (4) 2/(1 + x2) Solution: Let y =... View Article
If [latex]y=\sin^{-1}\left ( \frac{1-x^{2}}{{1+x^{2}}} \right )[/latex], then dy/dx equals
(1) 2/(1 – x2) (2) 1/(1 + x2) (3) -2/(1 + x2) (4) 2/(1 – x2) Solution: Given y =... View Article
If [latex]y=\tan^{-1}\left ( \frac{x}{\sqrt{1-x^{2}}} \right )[/latex], then dy/dx =
(1) -1/√(1 – x2) (2) x/√(1 – x2) (3) 1/√(1 – x2) (4) √(1 – x2)/x Solution: Given y =... View Article
Differential coefficient of cos-1 √x with respect to √(1 – x) is
(1) √x (2) -√x (3) 1/√x (4) -1/√x Solution: Let u = cos-1√x v = √(1 – x) Differentiate w.r.t.x... View Article
If [latex]f(x)=\cot^{-1}\left ( \frac{x^{x}-x^{-x}}{2} \right )[/latex], then f’(1) is equal to
(1) -1 (2) 1 (3) log 2 (4) -log 2 Solution: Given f(x) = cot-1 (xx – x-x)/2 = cot-1... View Article
If f(x) = x + 2, then f’(f(x)) at x = 4 is
(1) 8 (2) 1 (3) 4 (4) 5 Solution: Given f(x) = x + 2 f(f(x)) = x + 2... View Article
If y2 =ax2 + bx + c, then y3 d2y/dx2 is
(1) a constant (2) a function of x only (3) a function of y only (4) a function of x... View Article
If [latex]\Delta _{1}=\begin{vmatrix} x & a& b\\ b & x & a\\ a& b & x \end{vmatrix}[/latex] and [latex]\Delta _{2}=\begin{vmatrix} x & b\\ a& x \end{vmatrix}[/latex] are the given determinants, then
(1) ∆1 = 3(∆2)2 (2) d/dx ∆1 = 3(∆2) (3) d/dx ∆1 = 3(∆2)2 (4) ∆1 = 3(∆2)3/2 Solution: Given... View Article
If y = sin-1 √(1 – x2), then dy/dx =
(1) 1/√(1 – x2) (2) -1/√(1 – x2) (3) 1/√(1 + x2) (4) -1/√(x2 -1) Solution: Given y = sin-1... View Article
If [latex]y=\tan^{-1}\sqrt{\frac{a-x}{a+x}}[/latex], then dy/dx =
(1) cos-1(x/a) (2) -cos-1(x/a) (3) ½ cos-1(x/a) (4) none of these Solution: Given y = tan-1 √(a – x)/(a +... View Article
