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Recent questions tagged p110

Differentiate each of the following w.r.t $x$: $tan^{-1}\large\frac{3a^2x-x^3}{a^3-3ax^2}$, $\frac{1}{\sqrt 3}< \frac{x}{a} <\frac{-1}{\sqrt 3}$

asked Feb 19, 2013 by sreemathi.v

1 answer

If $x=3\sin t-\sin 3t,y=3\cos t-\cos 3t,find \;\large \frac{dy}{dx}\;\normalsize at \;t=\large \frac{\pi}{3}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=a\sin 2t(1+\cos 2t)\;and\;y=b\cos 2t(1-\cos 2t),show\;that\bigg(\large \frac{dy}{dx}\bigg)_{at\;t=\frac{\pi}{4}}=\frac{-b}{a}$

asked Dec 31, 2012 by sreemathi.v

1 answer

If $x=e^{\large\cos 2t}\; and\;y=e^{\large\sin 2t},prove\;that\;\large \frac{dy}{dx}=\frac{-ylog x}{xlog y}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=\large\frac{1+log t}{t^2},$$y=\large\frac{3+2log t}{t}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $\sin x=\large\frac{2t}{1+t^2},$$\tan y=\large\frac{2t}{1-t^2}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=3\cos \theta-2\cos^3\theta,y=3\sin \theta-2\sin^3\theta$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=e^\theta\bigg(\theta+\frac{1}{\theta}\bigg),y=e^{-\theta}\bigg(\theta-\frac{1}{\theta}\bigg)$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=t+\large\frac{1}{t},$$y=t-\large\frac{1}{t}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\tan^{-1}\Large {\bigg(\frac{\sqrt {1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\bigg)},\normalsize -1 < x < 1,x\neq 0$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sec^{-1}\bigg(\Large \frac{1}{4x^3-3x}\bigg),\normalsize 0 < x <\Large \frac{1}{\sqrt 2}$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x: $\tan^{-1}\bigg(\large {\frac {a \cos x - b \sin x}{b \cos x + a \sin x}}\bigg)$, where $\frac{-\pi}{2} < x < \frac{\pi}{2}$ and $\frac{a}{b} \tan x > -1$

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x:$\tan^{-1}(\sec x+\tan x),\large \frac{-\pi}{2}<$$x<\large\frac{\pi}{2}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t x:$\tan^{-1}\bigg(\sqrt{\large\frac{1-\cos x}{1+\cos x}}\bigg),$$\large\frac{-\pi}{4}<$$x<\large\frac{\pi}{4}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Differentiate the following w.r.t $x$ : $\sin^{-1} \big[\large\frac{1}{\sqrt 2}$$\sin x+\large\frac{1}{\sqrt 2}$$\cos x\big],\large\frac{-\pi}{4}<$$x<\large\frac{\pi}{4}$.

asked Dec 31, 2012 by sreemathi.v

1 answer

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