If x^p y^q = (x + y)^ p + q , then dy dx = - Vidyadip

MCQ

If ${x^p}{y^q} = {(x + y)^{p + q}},$ then ${{dy} \over {dx}} = $

✓
${y \over x}$
B
$ - {y \over x}$
C
${x \over y}$
D
$ - {x \over y}$

✓

Answer

Correct option: A.

${y \over x}$

a
(a) Taking $\log $ both sides,

$p\log x + q\log y = (p + q)\log (x + y)$

==> $\frac{p}{x} + \frac{q}{y}\frac{{dy}}{{dx}} = \frac{{p + q}}{{x + y}}\left( {1 + \frac{{dy}}{{dx}}} \right) $

$\Rightarrow \frac{{dy}}{{dx}} = \frac{y}{x}$.

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

A die is tossed thrice. A success is getting $1$ or $6$ on a toss. The mean and the variance of number of successes

If the three lines $x - 3y = p, ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then

A coin is tossed three times. Let X denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of $X$, then the value of $64\left(\mu+\sigma^2\right)$ is :

The coefficient of $x^{10}$ in the expansion of $(1 + x)^2 (1 + x^2)^3 ( 1 + x^3)^4$ is euqal to

If $y = {(\cos {x^2})^2}$ then ${{dy} \over {dx}}$ is equal to

Let the centre of a circle, passing through the point $(0,0),(1,0)$ and touching the circle $x^2+y^2=9$, be $(h, k)$. Then for all possible values of the coordinates of the centre $(h, k), 4\left(h^2+k^2\right)$ is equal to .............

If the point $(1 , a)$ lies between the straight lines $x + y = 1$ and $2(x + y) = 3$ then $a$ lies in interval

An orthogonal matrix is

In a triangle $PQR ,$ the co-ordinates of the points $P$ and $Q$ are $(-2,4)$ and $(4,-2)$ respectively. If the equation of the perpendicular bisector of $PR$ is $2 x-y+2=0,$ then the centre of the circumcircle of the $\Delta PQR$ is

For real $x$ with $-10 \leq x \leq 10$ define $f(x)=\int_{-10}^x 2^{[t]} d t$ where for a real number $r$ we denote by $[r]$ the largest integer less than or equal to $r$. The number of points of discontinuity of $f$ in the interval $(-10,10)$ is