Differentiation - Calculus - Mathematics Previous Year Questions

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1

-1

$\sinh x+x \cosh x$

$x \sinh x$

$\log \left(x+\sqrt{x^2+1}\right)$

$\frac{x\left(2 \sqrt{x^2-1}+1\right)}{\sqrt{x^2-1}\left(x^2+\sqrt{x^2-1}\right)}$

$\frac{2\left(3+2 t^5\right)}{\left(2-3 t^5\right)}$

$\frac{2 t\left(3-2 t^5\right)}{\left(2-3 t^5\right)}$

$\frac{2 t\left(3-2 t^5\right)}{\left(2+3 t^5\right)}$

$\frac{2\left(3+2 t^5\right)}{\left(2+3 t^5\right)}$

$\frac{2 x}{x^4+2 x^2+2}$

$-\frac{2 x}{x^4-2 x^2+2}$

$\frac{2 x}{x^4-2 x^2+2}$

$-\frac{2 x}{x^4+2 x^2+2}$

$\frac{2 \cos 5 \theta+\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$

$\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}$

$\frac{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}$

$\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$

$\frac{2 x y}{\left(1+x^2\right)^2}$

$-\frac{(x+y)}{\left(1-x^2\right)^2}$

$\frac{2(x y)}{1-x^2}$

$-\frac{2(x+y)}{1-x^2}$

-3

3

$-\frac{1}{3}$

$\frac{1}{3}$

$\frac{2}{\pi}$

$\frac{\pi-2}{2}$

$\frac{2}{\pi-2}$

$\frac{\pi}{2}$

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