If y= 1+1 x^ 2 1-1 x^ 2 then dy dx is equal to: - Vidyadip

MCQ

If $\text{y}=\frac{1+\frac{1}{\text{x}^{2}}}{1-\frac{1}{\text{x}^{2}}}$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:

✓
$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
B
$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
C
$\frac{1-\text{x}^{2}}{4\text{x}}$
D
$\frac{4\text{x}}{\text{x}^{2}-1}$

✓

Answer

Correct option: A.

$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$

Given, $\text{y}=\frac{1+\frac{1}{\text{x}^{2}}}{1-\frac{1}{\text{x}^{2}}}$
$\Rightarrow\text{y}=\frac{\text{x}^{2}+1}{\text{x}^{2}-1}$
$\therefore \frac{\text{dy}}{\text{dx}}=\frac{(\text{x}^{2}-1).2\text{x}-(\text{x}^{2}+1).2\text{x}}{(\text{x}^{2}-1)^{2}}$
$=\frac{2\text{x}(\text{x}^{2}-1-\text{x}^{2}-1)}{(\text{x}^{2}-1)^{2}}$
$=\frac{2\text{x}(-2)}{(\text{x}^{2}-1)^{2}}$
$=\frac{-4\text{x}}{(\text{x}^{2}-1)^2{}}$

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

More "M.C.Q (1 Marks)" from Limits and Derivatives→Limits and Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If the length of the tangent from the origin to the circle centered at $(2, 3)$ is $2$ then the equation of the circle is:

Find the value of $\sec \left(\frac{-19 \pi}{3}\right)$.

If $\tan ( A + B )=p$ and $\tan ( A - B )=q$, then the value of $\tan 2 A$ in terms of $p$ and $q$ is :

What is the locus of a point for which $y = 0, z = 0?$

The value of $\lim _{m \rightarrow \infty}\left(1-\frac{1}{m}\right)^{-m}$ is equal to :

If $49^n+ 16^n+ k$ is divisible by $64$ for $n \in N,$ then the least negative integral value of $k$ is:

Let the common tangents to the curves $4\left(x^{2}+y^{2}\right)=$ $9$ and $y ^{2}=4 x$ intersect at the point $Q$. Let an ellipse, centered at the origin $O$, has lengths of semi-minor and semi-major axes equal to $OQ$ and $6$ , respectively. If $e$ and $l$ respectively denote the eccentricity and the length of the latus rectum of this ellipse, then $\frac{l}{ e ^{2}}$ is equal to

If $\text{A}\cap\text{B}=\text{B},$ then:

Let $P : y ^{2}=4 a x , a>0$ be a parabola with focus $S$.Let the tangents to the parabola $P$ make an angle of $\frac{\pi}{4}$ with the line $y=3 x+5$ touch the parabola $P$ at $A$ and $B$. Then the value of $a$ for which $A , B$ and $S$ are collinear is

The urns $A, B$ and $C$ contain $4$ red, $6$ black;$5$ red,$5$ black and $\lambda$ red,$4$ black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn $C$ is $0.4$ then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola $y^2=\lambda x$ with one vertex at the vertex of the parabola is