Download App

STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
${d \over {dx}}\left( {{{{{\cot }^2}x - 1} \over {{{\cot }^2}x + 1}}} \right) = $
  • A
    $ - \sin 2x$
  • B
    $2\sin 2x$
  • C
    $2\cos 2x$
  • ✓
    $ - 2\sin 2x$
✓

Answer

Correct option: D.
$ - 2\sin 2x$
d
(d) $\frac{d}{{dx}}\left[ {\frac{{{{\cot }^2}x - 1}}{{{{\cot }^2}x + 1}}} \right] = \frac{d}{{dx}}\left[ {\frac{{{{\cos }^2}x - {{\sin }^2}x}}{{{{\cos }^2}x + {{\sin }^2}x}}} \right]$

$ = \frac{d}{{dx}}[\cos 2x] = - 2\sin 2x$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\tan x = \frac{{2b}}{{a - c}}(a \ne c),$

$y = a\,{\cos ^2}x + 2b\,\sin x\cos x + c\,{\sin ^2}x$

and $z = a{\sin ^2}x - 2b\sin x\cos x + c{\cos ^2}x,$ then

→
The relation "is subset of" on the power set $P(A)$ of a set $A$ is
→
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point $0, 1$ and $2$ are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are independents, the probability of India getting at least $7$ points is
→
If $\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-x+1}-a x\right)=b$, then the ordered pair $(a, b)$ is:
→
Let $A_{1}, A_{2}, A_{3}, \ldots \ldots . .$ be squares such that for each $n \geq 1,$ the length of the side of $A _{ n }$ equals the length of diagonal of $A _{ n +1}$. If the length of $A _{1}$ is $12\, cm ,$ then the smallest value of $n$ for which area of $A _{ n }$ is less than one, is ..........
→
Let $S=\left\{\theta \in(0,2 \pi): 7 \cos ^{2} \theta-3 \sin ^{2} \theta-2\right.$ $\left.\cos ^{2} 2 \theta=2\right\}$. Then, the sum of roots of all the equations $x ^{2}-2\left(\tan ^{2} \theta+\cot ^{2} \theta\right) x +6 \sin ^{2} \theta=0$ $\theta \in S$, is$...$
→
Consider the set of all triangle $OPQ$ where $'O'$ is origin and $P$, $Q$ are distinct points in the plane with non - negative integral co-ordinates $(x,y)$ such that $5x + y = 99$, then  the number of such distinc triangle whose area is positive integer, are
→
On which of the following intervals, the function $x^{100} + sin x - 1$ is strictly increasing.
→
Let the image of the point $(1,0,7)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ be the point $(\alpha, \beta, \gamma)$. Then which one of the following points lies on the line passing through $(\alpha, \beta, \gamma)$ and making angles $\frac{2 \pi}{3}$ and $\frac{3 \pi}{4}$ with $y$-axis and $z$-axis respectively and an acute angle with $\mathrm{x}$-axis?
→
If $\frac{{3 + 5 + 7 + ..........{\rm{to}}\;n\;{\rm{terms}}}}{{5 + 8 + 11 + .........{\rm{to}}\;10\;{\rm{terms}}}} = 7$, then the value of $n$ is
→