Recent questions tagged p191

If $( x-a)^2 + (y-b)^2 = c^2$, for some $ c > 0$, prove that $\Large\frac{\begin{bmatrix} 1 + \left(\frac{dy}{dx}\right)^2 \\[0.3em] \end{bmatrix}^{\frac{\Large 3}{\Large 2}}}{\Large\frac{d^2y}{dx^2}}$is a constant independent of $a$ and $b$.

asked Nov 21, 2012 by thanvigandhi_1

1 answer

If $ x \sqrt {1+y} + y \sqrt{1+x} = 0$, for, $-1 < x < 1$, prove that $\large \frac{dy}{dx} = -\frac{1}{(1+x)^2} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Find $\large \frac{dy}{dx} $, if $ y = \sin^{-1}x + \sin^{-1} \: \sqrt {1-x^2} , -1 \leq x \leq 1 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Find $ \large\frac{dy}{dx} $, if $ y = 12 ( 1 - \cos t ) , x = 10 ( t - \sin t ) , -\large\frac{\pi}{2}\normalsize < t <\large \frac{\pi}{2} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ x^{\large x^2-3} + ( x - 3 )^{\large x^2} $, for $x > 3$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ x^{\large x} + x^{\large a} + a^{\large x} + a^{\large a} $, for some fixed $ a > 0 $ and $ x > 0 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ (\sin x - \cos x )^{\large(\sin x - \cos x )} , \large\frac {\pi}{4}\normalsize < x < \large\frac{3\pi}{4} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ \cos \: (a \cos x + b \sin x) $ , for some constant $a$ and $b$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $( \log x )^{\large\log x}, x > 1 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $\large\frac{\cos^{ -1}\Large\frac{ x}{ 2}}{\sqrt {2x + 7}}, \normalsize-2 < x < 2 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ sin^{-1}(x \: \sqrt x ), 0 \leq x \leq 1 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $(5x)^{\large 3 \cos 2x} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ sin^3x + cos^6x $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Differentiate w.r.t. $x$ the function in $ (3x^2 - 9x + 5)^9 $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

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If \(( x-a)^2 + (y-b)^2 = c^2\), for some \( c > 0\), prove that $\Large\frac{\begin{bmatrix} 1 + \left(\frac{dy}{dx}\right)^2 \\[0.3em] \end{bmatrix}^{\frac{\Large 3}{\Large 2}}}{\Large\frac{d^2y}{dx^2}}$is a constant independent of \(a\) and \(b\).

If \( x \sqrt {1+y} + y \sqrt{1+x} = 0\), for, \(-1 < x < 1\), prove that $\large \frac{dy}{dx} = -\frac{1}{(1+x)^2} $

Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$

Find \(\large \frac{dy}{dx} \), if \( y = \sin^{-1}x + \sin^{-1} \: \sqrt {1-x^2} , -1 \leq x \leq 1 \)

Find \( \large\frac{dy}{dx} \), if \( y = 12 ( 1 - \cos t ) , x = 10 ( t - \sin t ) , -\large\frac{\pi}{2}\normalsize < t <\large \frac{\pi}{2} \)

Differentiate w.r.t. \(x\) the function in \( x^{\large x^2-3} + ( x - 3 )^{\large x^2} \), for \(x > 3\)

Differentiate w.r.t. \(x\) the function in \( x^{\large x} + x^{\large a} + a^{\large x} + a^{\large a} \), for some fixed \( a > 0 \) and \( x > 0 \)

Differentiate w.r.t. \(x\) the function in \( (\sin x - \cos x )^{\large(\sin x - \cos x )} , \large\frac {\pi}{4}\normalsize < x < \large\frac{3\pi}{4} \)

Differentiate w.r.t. \(x\) the function in \( \cos \: (a \cos x + b \sin x) \) , for some constant \(a\) and \(b\)

Differentiate w.r.t. \(x\) the function in \(( \log x )^{\large\log x}, x > 1 \)

Differentiate w.r.t. \(x\) the function in \(\large\frac{\cos^{ -1}\Large\frac{ x}{ 2}}{\sqrt {2x + 7}}, \normalsize-2 < x < 2 \)

Differentiate w.r.t. \(x\) the function in \( sin^{-1}(x \: \sqrt x ), 0 \leq x \leq 1 \)

Differentiate w.r.t. $x$ the function in $(5x)^{\large 3 \cos 2x} $

Differentiate w.r.t. \(x\) the function in \( sin^3x + cos^6x \)

Differentiate w.r.t. \(x\) the function in \( (3x^2 - 9x + 5)^9 \)