Question:
if $(xe)^y = e^x$, then $\frac{dy}{dx}$ is =
if $(xe)^y = e^x$, then $\frac{dy}{dx}$ is =
Updated On: May 19, 2024
- $\frac {log x}{ (1+logx)^2}$
- $\frac {1}{ (1+logx)^2}$
- $\frac {log x}{ (1+logx)}$
- $\frac {e^x}{ x(y-1)}$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
$(x e)^{y}=e^{x}$
$\Rightarrow y(\log x+1)=x$
$\Rightarrow y=x /(\log x+1)$
$\therefore \left(\frac{dy}{dx} = \frac{log \ x}{(log \ x + 1)^2}\right)$
$\Rightarrow y(\log x+1)=x$
$\Rightarrow y=x /(\log x+1)$
$\therefore \left(\frac{dy}{dx} = \frac{log \ x}{(log \ x + 1)^2}\right)$
Was this answer helpful?
1
3
Top Questions on Derivatives of Functions in Parametric Forms
- The area of the region under the curve \( y = |\sin x - \cos x| \) in the interval \( 0 \leq x \leq \frac{\pi}{2} \), above the x-axis, is (in square units):
- AP EAMCET - 2024
- Mathematics
- Derivatives of Functions in Parametric Forms
- If \( f(x) = x^x \), then the interval in which \( f(x) \) decreases is:
- AP EAMCET - 2024
- Mathematics
- Derivatives of Functions in Parametric Forms
- If \( a \) is in the 3rd quadrant, \( \beta \) is in the 2nd quadrant such that \( \tan \alpha = \frac{1}{7}, \sin \beta = \frac{1}{\sqrt{10}} \), then \[ \sin(2\alpha + \beta) = \]
- AP EAMCET - 2024
- Mathematics
- Derivatives of Functions in Parametric Forms
- If the lines \( \frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4} \) and \( \frac{x-3}{1} = \frac{y - 9/2}{2} = z/1 \) intersect, then the value of \( k \) is:
- MHT CET - 2024
- Mathematics
- Derivatives of Functions in Parametric Forms
- If \( 2 \tan^2 \theta - 5 \sec \theta = 1 \) has exactly 7 solutions in the interval \(\left[ 0, \frac{n\pi}{2} \right],\) for the least value of \( n \in \mathbb{N} \) then \(\sum_{k=1}^{n} \frac{k}{2^k}\) is equal to:
- JEE Main - 2024
- Mathematics
- Derivatives of Functions in Parametric Forms
View More Questions
Questions Asked in KCET exam
- The electric current flowing through a given conductor varies with time as shown in the graph below. The number of free electrons which flow through a given cross-section of the conductor in the time interval \( 0 \leq t \leq 20 \, \text{s} \) is
- KCET - 2024
- Current electricity
- A die is thrown 10 times. The probability that an odd number will come up at least once is:
- KCET - 2024
- Probability
- The incorrect statement about the Hall-Heroult process is:
- KCET - 2024
- General Principles and Processes of Isolation of Elements
- Corner points of the feasible region for an LPP are $(0, 2), (3, 0), (6, 0), (6, 8)$ and $(0, 5)$. Let $z = 4x + 6y$ be the objective function. The minimum value of $z$ occurs at:
- KCET - 2024
- Linear Programming Problem
- If a random variable $X$ follows the binomial distribution with parameters $n = 5$, $p$, and $P(X = 2) = 9P(X = 3)$, then $p$ is equal to:
- KCET - 2024
- binomial distribution
View More Questions