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

Question

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

✓

Answer

(c) : We have, $x^y=e^{x-y}$
Taking $\log$ on both sides, we get
$
y \log x=(x-y) \log e \Rightarrow y=\frac{x}{1+\log x}
$
Differentiating w.r.t. $x$, we get
$
\frac{d y}{d x}=\frac{(1+\log x)-x \cdot \frac{1}{x}}{(1+\log x)^2}=\frac{\log x}{(1+\log 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 Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

What is the length of the longer diagonal of the parallelogram constructed on $5\vec{\text{a}}+2\vec{\text{b}}$ and $\vec{\text{a}}-3\vec{\text{b}}$ if it is given that $|\vec{\text{a}}|=2\sqrt{2},\big|\vec{\text{b}}\big|=3$ and the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ is $\frac{\pi}{4}$?

$15$
$\sqrt{113}$
$\sqrt{593}$
$\sqrt{369}$

If the projections of the line segment $AB$ on the coordinate axes are $12, 3, k$ and $AB = 13$ then $k^2 - 2k + 3$ is equal to$:$

The order of a matrix $\begin{bmatrix}2&\text{amp};5 &\text{amp};7 \end{bmatrix}$ is:

3 × 3
1 × 1
3 × 1
1 × 3

Which of the following statements about an LP problem and its dual is false?

The value of $\int \frac{1}{e^x+e^{-x}} d x$ is

Find the cofactors of elements $a_{12}, a_{22}, a_{32}$ respectively of the matrix $\left[\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right]$.

The set points where the function f(x) given by $\text{f(x)=}|\text{x}-3|\cos\text{x}$ is diffrentiable, is:

R
R - {3}
$(0,\infty)$
None of these.

The area bounded by the curves $\text{y}=\sin\text{x},\text{y}=\cos\text{x}$ y − axes in first quadrant is:

$\sqrt{2}-1$
$\sqrt{2}$
$\sqrt{2}+1$
$\text{none}\text{ of}\text{ the}\text{ above}$

A function $f: R \rightarrow R$ is defined such that $f(x)=x^3$ +1 , then function :

The area between x-axis and curve $\text{y}=\cos\text{x}$ when $0\leq\text{x}\leq2\pi$ is:

0
2
3
4