If y = (_e x)^_e x, then dy/dx is equal to: Option 1: _e x (_e x)^_e x - 11/x Option 2: 1(_e x)^_e x[1+_e(_e x)/x] Option 3: (1/x)^1/x Option 4: (_e x)^_e x[1+_e(_e x)/x]

The answer is '(_e x)^_e x[1+_e(_e x)/x]'. View full solution:

CUET Mathematics - If y = (_e x)^_e x, then dy/dx is equal to: | PYQs + Solutions

CUET Mathematics 2026 26th May Shift 2

Calculus

Medium

core

$\log_e x (\log_e x)^{\log_e x - 1}\dfrac{1}{x}$

$\dfrac{1}{(\log_e x)^{\log_e x}}\left[\dfrac{1+\log_e(\log_e x)}{x}\right]$

$\left(\dfrac{1}{x}\right)^{1/x}$

$(\log_e x)^{\log_e x}\left[\dfrac{1+\log_e(\log_e x)}{x}\right]$

✅ Correct Option: 4

Related questions:

21 May Shift 1

If $y = t - \frac{1}{t}$ and $x = t + \frac{1}{t}$ , then $\frac{dy}{dx}$ is equal to

26th May Shift 2

Let $f(x) = |3-x| + (3+x)$ be a function, then which of the following statements are TRUE?

A. $f(x)$ is continuous at $x=3$

B. $f(x)$ is continuous at $x=-3$

C. $f(x)$ is differentiable at $x=3$

D. $f(x)$ is differentiable at $x=-3$

Choose the correct answer from the options given below:

22 May Shift 3

Match List - I with List - II.

Choose the correct answer from the options given below :