If x = e^(y + e^(y + e^(y + ∞))), x > 0, then dy/dx is equal to Option 1: x/(1+x) Option 2: 1/x Option 3: (1-x)/x Option 4: (1+x)/x

Answer: (1-x)/x. Solution: By the recursive structure, x = e^(y+x). Taking log: x = y + x, so y = x - x. Differentiating: dy/dx = 1/x - 1 = (1-x)/x.

Calculus

Continuity & Differentiability

Medium

If $x = e^{y + e^{y + e^{y + \ldots \infty}}}$ , $x > 0$ , then $\frac{dy}{dx}$ is equal to

$\frac{x}{1+x}$

$\frac{1}{x}$

$\frac{1-x}{x}$

$\frac{1+x}{x}$

✅ Correct Option: 3

By the recursive structure, $x = e^{y+x}$ .

Taking log: $\ln x = y + x$ , so $y = \ln x - x$ .

Differentiating: $\frac{dy}{dx} = \frac{1}{x} - 1 = \frac{1-x}{x}$ .

2026: 15 May Shift 1

Match the LIST-I with LIST-II

LIST-I (Function in parametric form)	LIST-II ( $\dfrac{dy}{dx}=$ )
A. $x=t, y=t$	I. 1
B. $x=t^2, y=2t$	II. $\dfrac{1}{t}$
C. $x=3t, y=t^2$	III. $\dfrac{2t}{3}$
D. $x=2t, y=3t^2$	IV. $3t$

Choose the correct answer from the options given below:

2025: 3 June Shift 2

If $x^m y^n = (x + y)^{m+n}$ , then $\frac{d^2y}{dx^2}$ is equal to:

2026: 19 May Shift 1

If $y = 500e^{7x} + 600e^{-7x}$ , then $\frac{d^2y}{dx^2}$ equals :

2026: 30 May Shift 1

Let $f(x)=\begin{cases}\frac{1-\cos4x}{x^2}, & \text{if } x<0\\2\lambda, & \text{if } x=0\\\frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & \text{if } x>0\end{cases}$ such that $f$ continuous at $x=0$ . Then, the value of $\lambda$ is equal to:

2025: 15 May Shift 2

The value of k for which the function, defined by, $f(x) = \begin{cases} \frac{3x + 4 \tan x}{x} & : x \neq 0 \\ k & : x = 0 \end{cases}$ is continuous at $x = 0$ , is

2022: 25 May Shift 1

If $\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y)$ , then $\frac{dy}{dx} =$

If x=ey+ey+ey+…∞x = e^{y + e^{y + e^{y + \ldots \infty}}}x=ey+ey+ey+…∞, x>0x > 0x>0, then dydx\frac{dy}{dx}dxdy​ is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $x = e^{y + e^{y + e^{y + \ldots \infty}}}$ , $x > 0$ , then $\frac{dy}{dx}$ is equal to