Recent questions tagged ch5

If $ y = 3 \cos \: (\log x ) + 4 \sin ( \log x )$, show that $x^2y_2 + xy_1 + y = 0$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y =\cos^{-1}x $ , find $ \large\frac{d^2y}{dx^2}$ in terms of $ y $ alone.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $ y = 5 \cos x - 3 \sin x $ , prove that $ \large\frac{d^2y}{dx^2}\normalsize + y = 0$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ \sin (\log x) $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $\log ( \log x) $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ \tan^{-1} x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of $ e^{6x} \cos 3x$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the function $(e^{\large x} \sin 5x)$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^3 \log x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $\log x $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x \; \cos x$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^{\large 20} $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^2 + 3x + 2 $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x = \sqrt {a^{\large sin^{-1}t}}, \: y = \sqrt {a^{\large cos^{-1}t}} $, show that $\frac {\large dy}{\large dx} = -\frac{\large y}{\large x} $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = a ( \cos \theta + \theta \sin \theta), y = a ( \sin \theta - \theta \cos \: \theta) $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = a \sec \theta, y = b \tan \theta $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = a \big(\cos t +\ log \tan \large\frac{t}{2}\big) $ and $ y = a \sin t $ without eliminating the parameter, Find $ \frac{\large dy}{\large dx}$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \large\frac{\sin^3t}{\sqrt {\cos 2t}}, $$y = \large\frac{\cos^3t}{\sqrt {\cos 2t}} $ without eliminating the parameter, Find $\large\frac{ dy}{ dx}$.

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = a ( \theta - \sin \theta ), y = a ( 1 +\cos \theta) $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \cos \theta -\ cos 2\theta, y = \sin \theta -\ sin 2\theta $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = 4t, \: y = \large\frac{4}{t} $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \sin t, y = \cos 2t $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = a \cos \theta, y = b \cos \theta $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = 2at^2, \: y = at^4 $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

If $u,\: v$ and $w$ are functions of $x$, then show that $\large\frac{d}{dx} $$( u.v.w) =\large \frac{du}{dx} $$v.w + u . \large\frac{dv}{dx} $$. w + u.v. \large\frac{dw}{dx} $ in two ways - first by repeated application of product rule, second by logarithmic differentiation.

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate $ (x^2 - 5x + 8) (x^3 + 7x + 9 ) $ in three ways mentioned below:\begin{array}{1 1} (i)\;by\;using\;product\;rule & \;\\(ii)\;by\;expanding\;the\;product\;to\;obtain\;a\;single\;polynomial. & \;\\ (iii)\;by\;logarithmic\;differentiation. & \;\end{array} Do they all give the same answer?

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find the derivative of the function given by $f(x) =( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)$ and hence find $ f' (1).$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the function $xy = e^{\large(x-y)}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the function $(\cos x)^{\large y} = (\cos y)^{\large x}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the functions given in $ y^{\large x} = x^{\large y} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find $\large\frac{dy}{dx}$ of the functions given in $ x^{\large y }+ y^{\large x }= 1 $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x \cos x )^{\large x} + (x\sin x)^{\Large\frac{1}{x}} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x^{\large x \cos x} + \large\frac{x^2 + 1}{x^2 - 1} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x ^{\large\sin x} + (\sin x)^{\large\cos x} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x$ : $ (\sin x )^{\large x} + \sin^{-1} \sqrt x $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $y=(\log x)^{\large x}+x^{\large\log x}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x + \large\frac{1}{x})^{\large x}$$ + x ^{\large (1 + \Large\frac{1}{x})} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x + 3)^2 \: . \: (x + 4)^3 \: . \: (x + 5)^4 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x^{\large x} - 2^{\large sin \: x} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ ( \log \; x )^{\large cos \: x} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x :$ $ \sqrt {\large\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ \cos \: x \: . \cos \: 2x \:. \cos \: 3x $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $ x: $ $ cos \: ( log\: x + e^x ), x > 0 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x: \large \frac {\cos x}{\log x}$,$\; x > 0 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x :$$ log ( log \: x ), x > 1 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : \sqrt {e^\sqrt x}, x > 0 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : e^x + e^{x^2} + \: ... + e^{x^5} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : \log\;( cos \: e^x ) $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : sin\;( tan^{-1} e^{-x}) $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : e^{x^{3} } $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

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