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Questions >> CBSE XII >> Math >> Continuity and Differentiability

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

Differentiate the following w.r.t. $x : e^{sin^{-1} x}$

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : \large \frac{e^x}{sin\;x}$

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Find $\large \frac {dy}{dx}$ in the following: $y = sec^{-1} \left(\large\frac{1}{2x^2 - 1}\right), 0 < x < \; { \frac{1}{\sqrt2} } \\$

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Find $\large \frac {dy}{dx}$ in the following: $y = \sin^{-1} \big( 2x \sqrt{1 -x^2} \big), -\;{ \frac{1}{\sqrt2} }\;< x < \;{\frac{1}{\sqrt2} }\\$

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Find $\large\frac {dy}{dx}$ in the following: $y = cos^{-1} \left(\large\frac{2x}{1 + x^2}\right), -1 < x < 1$

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $y = sin^{-1} \left(\frac{1 - x^2}{1 + x^2}\right), 0 < x < 1$

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $y = cos^{-1} \left(\frac{1 - x^2}{1 + x^2}\right), 0 < x < 1$

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $y = tan^{-1} \left(\frac{3x - x^3}{1 - 3x^2}\right), - \; { \frac{1}{\sqrt3} } < x < \;{\frac{1}{\sqrt3} }\\$

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $y = sin^{-1} \left(\frac{2x}{1 + x^2}\right)$

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $\sin^2x +\cos^2y = 1$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $sin^2y + cos \: xy = k$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $x^3 +x^2y + xy^2 +y^3 = 81$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $x^2 +xy + y^2 = 100$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $xy +y^2 = tan \: x + y$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $ax +by^2 = cos \: y$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $2x +3y = sin \: y$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find $\frac {dy}{dx}$ in the following: $2x +3y = sin \: x$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $f(x) = \left\{ \begin{array} {1 1} \large\frac{k\cos x}{\pi - 2x}\normalsize,& \quad { if \; x \neq \large\frac{\pi}{2} }\\ \normalsize 3 ,& \quad { if \; x = \large\frac{\pi}{2} }\\ \end{array} \right. \qquad at \; x = \; \large\frac{\pi}{2}$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $a$ and $b$ such that the function defined by $f(x) = \left\{ \begin{array} {1 1} 5 ,& \quad\text{ if $ x $ \(\leq 2\)}\\ ax+b,& \quad \text{if $2$ < x<10}\\ 21,& \quad \text{if $ x $ \(\geq 10\)}\\ \end{array} \right.$ is a continuous function.

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ \(\leq 5\)}\\ 3x-5,& \quad \text{if $x$ > 5}\\ \end{array} \right.\qquad at \; x = 5$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $f(x) = \left\{ \begin{array} {1 1} kx+1 ,& \quad\text{ if $ x $ \(\leq \pi\)}\\ \cos x,& \quad \text{if $x$ > \(\pi\)}\\ \end{array} \right.$ at $x = \pi$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find the values of $k$ so that the function $f$ is continuous at the indicated point in $f(x) = \left\{ \begin{array} {1 1} kx^2 ,& \quad\text{ if $ x $ \(\leq 2\)}\\ 3,& \quad \text{if $x$ > 2}\\ \end{array} \right. \qquad at \;x = 2$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

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