CUET Mathematics - If y = 3^x + e^x + x^x + x^3, then the value of dy/dx at x = 3 is | PYQs + Solutions

CUET Mathematics 2025 13 May Shift 1

Calculus

Medium

core

$e^3 + 27\log_e 3 + 27$

$e^3 + 54\log_e 3 + 54$

$e^3 + 54\log_e 3 + 27$

$e^3 + 27\log_e 3 + 54$

✅ Correct Option: 2

Related questions:

14 May Shift 2

Match List-I with List-II

List-I	List-II
Function	Derivative
(A) $y = \sin^{-1} x + \sin^{-1} \sqrt{1 - x^2}; \|x\| < 1$	(I) $\frac{dy}{dx} = \frac{1}{2y-1}$
(B) $y = \sqrt{x + y}, x+y > 0 \text{ and } y \neq \frac{1}{2}$	(II) $\frac{dy}{dx} = 10^x \log_e 10$
(C) $y = \log_{10} x, x > 0$	(III) $\frac{dy}{dx} = 0$
(D) $y = 10^x$	(IV) $\frac{dy}{dx} = \frac{1}{x \log_e 10}$

Choose the correct answer from the options given below:

3 June Shift 2

Let

$f(x)=\begin{cases} |x|+3 & \text{if } x\le -3 \\ -2x & \text{if } -3<x<3 \\ 6x+2 & \text{if } x\ge 3 \end{cases}$

Then, which of the following is true?

3 June Shift 1

If $e^y(x + 1) = 1$ and $\frac{d^2y}{dx^2} = k(\frac{dy}{dx})^2$ , then k is equal to

CUET Mathematics 2025 13 May Shift 1 PYQs