x1 + y + y1 + x = 0, then dy dx = - Vidyadip

MCQ

$x\sqrt {1 + y} + y\sqrt {1 + x} = 0$, then ${{dy} \over {dx}} = $

A
$1 + x$
B
${(1 + x)^{ - 2}}$
C
$ - {(1 + x)^{ - 1}}$
✓
$ - {(1 + x)^{ - 2}}$

✓

Answer

Correct option: D.

$ - {(1 + x)^{ - 2}}$

d
(d) $x\sqrt {1 + y} + y\sqrt {1 + x} = 0$ $\Rightarrow$ ${x^2}(1 + y) = {y^2}(1 + x)$

$\Rightarrow$ $(x-y)(x+y+xy)=0$ $\Rightarrow$ $x+y+xy=0,$ $\,\,\,\left\{ \because x\ne y \right\}$

$\Rightarrow$ $\frac{{dy}}{{dx}} = \frac{{ - 1}}{{{{(1 + x)}^2}}}$.

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 STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Minimise $\text{Z}=\sum\limits^{\text{n}}_{\text{j}=1}\sum\limits^{\text{m}}_{\text{i}=1}\text{c}_{\text{ij}}\cdot\text{x}_{\text{ij}}$ Subject to $\sum\limits^{\text{m}}_{\text{i}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,....\text{n}$ $\sum\limits^{\text{n}}_{\text{j}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,.....,\text{m}$ is a $\text{LPP}$ with number of constraints.

The value of $\big(\vec{\text{a}}\times\vec{\text{b}}\big)^2$ is:

The value of the determinant $\begin{vmatrix}\text{x}&\text{x}+\text{y}&\text{x}+2\text{y}\\\text{x}+2\text{y}&\text{x}&\text{x}+\text{y}\\\text{x}+\text{y}&\text{x}+2\text{y}&\text{x}\end{vmatrix}$ is:

For each real number $x$, let $[ x ]$ denote the greatest integer less than or equal to $x$, and let $\{ x \}= x -[ x ]$. Then the smallest positive integer $M$ for which $\int_1^M\{x\}^{[x]} d x > 1$ is

A cone of maximum volume is inscribed in a given sphere, then ratio of the height of the cone to diameter of the sphere is

If $I=\sum_{k=1}^{98} \int_k^{k+1} \frac{k+1}{x(x+1)} d x$, then $[A]$ $I>\log _e 99$ $[B]$ $I<\log _e 99$ $[C]$ $I<\frac{49}{50}$ $[D]$ $I>\frac{49}{50}$

If the area of the region

$\left\{(\mathrm{x}, \mathrm{y}): \frac{\mathrm{a}}{\mathrm{x}^2} \leq \mathrm{y} \leq \frac{1}{\mathrm{x}}, 1 \leq \mathrm{x} \leq 2,0<\mathrm{a}<1\right\}$ is

$\left(\log _e 2\right)-\frac{1}{7}$ then the value of $7 a-3$ is equal to:

Let $A=\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right] .$ Then the number of $3 \times 3$ matrices $\mathrm{B}$ with entries from the set $\{1,2,3,4,,5\}$ and satisfying $A B=B A$ is $....$

$A$ and $B$ are two students. Their chances of solving a problem correctly are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability of their making common error is $\frac{1}{20}$ and they obtain the same answer, then the probability of their answer to be correct is.

Let $A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$. Let $\alpha, \beta \in R$ be such that $\alpha A^{2}+\beta A=2 I$. Then $\alpha+\beta$ is equal to -