If x^y=y^ x , then d y d x = - Vidyadip

MCQ

If $x^y=y^{ x }$, then $\frac{d y}{d x}=$

A
$\frac{x(x \log y-y)}{y(y \log x-x)}$
✓
$\frac{y(y \log x-x)}{x(x \log y-y)}$
C
$\frac{y^2(1-\log x)}{x^2(1-\log y)}$
D
$\frac{y(1-\log x)}{x(1-\log y)}$

✓

Answer

Correct option: B.

$\frac{y(y \log x-x)}{x(x \log y-y)}$

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 "MCQ" from Differentiation→Differentiation — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\tan ^{-1} 2 x+\tan ^{-1} 3 x=\frac{\pi}{4}$, then $x=$

Equation of the plane passing through points $(1,-1,3)$ and $(2,3,-4)$ and parallel to $X$-axis is

A r.v. $X \sim B(n, p)$. If value of mean and variance of $X$ are 18 and 12 respectively, then total number of possible values of $X$ are

$Q^+$ denote the set of all positive rational numbers. If the binary operation $\text{a }\odot$ on $Q^+$ is defined as:
$\text{a }\odot=\frac{\text{ab}}{2}$, then the inverse of $3$ is:

The direction ratios of two lines are $a, b, c$ and $\frac{1}{ bc }, \frac{1}{ ca }, \frac{1}{ ab }$. The lines are

The value of $\int\limits^{\pi}_0\frac{1}{5+3\cos\text{x}}\text{ dx}$ is:

The value of $\int_0^\pi e ^{\cos ^2 x} \cos ^5 3 x d x$ is

Area bounded by the curve $x^2=4 y$ and the straight line $x=4 y-2$ is

If direction ratios of two lines are $5,-12,13$ and $-3,4,5$, then the angle between them is

If $A=\left[\begin{array}{ll}4 & 2 \\ 3 & 4\end{array}\right]$, then $|\operatorname{adj} A|$ is equal to