If y = _3(_3 x), then dy/dx Option 1: 1/(x 3x) Option 2: 1/(x(x 3 + x)) Option 3: ()/(x 3) Option 4: 1/(x x 3)

Answer: 1/(x x 3). Solution: y = _3(_3 x) = ((_3 x))/( 3) = 1/( 3)[( x) - ( 3)]. dy/dx = 1/( 3) * 1/( x) * 1/x = 1/(x x 3). This matches option (4) where the denominator includes x, log x, and log 3.

Applied Mathematics

Calculus

Hard

If $y = \log_3(\log_3 x)$ , then $\frac{dy}{dx}$

$\frac{1}{x\log 3x}$

$\frac{1}{x(x\log 3 + \log x)}$

$\frac{\log}{x\log 3}$

$\frac{1}{x\log x \log 3 }$

✅ Correct Option: 4

$y = \log_3(\log_3 x) = \frac{\log(\log_3 x)}{\log 3} = \frac{1}{\log 3}[\log(\log x) - \log(\log 3)]$ .

$\frac{dy}{dx} = \frac{1}{\log 3} \cdot \frac{1}{\log x} \cdot \frac{1}{x} = \frac{1}{x \log x \log 3}$ .

This matches option (4) where the denominator includes x, log x, and log 3.

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Differential equation)		LIST-II (Degree)
A.	$\left(\dfrac{dy}{dx}\right)^2 + \dfrac{1}{\dfrac{dy}{dx}} = 5$	I.	$2$
B.	$\dfrac{d^3y}{dx^3} = \left\{3 + \left(\dfrac{dy}{dx}\right)^2\right\}^{3/2}$	II.	$4$
C.	$\dfrac{d^2y}{dx^2} = \left(\dfrac{dy}{dx}\right)^{5/4}$	III.	$1$
D.	$y\dfrac{d^2x}{dy^2} = y^2 + 1$	IV.	$3$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

If $x = 3at^2$ , $y = 3at^4$ then $\frac{dy}{dx}$ is :

2023: 30 May Shift 3

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :

2022: 25 May Shift 1

If $f(x) = a\log|x| + \dfrac{b}{x} + x$ has its extreme values at $x = -1$ and $x = 3$ , then $(a, b)$ is equal to:

2023: 30 May Shift 3

Match List - I with List - II.

List - I (Functions)	List - II (Maximum value)
(A) $f(x) = -x^2, x \in (-\infty, \infty)$	(I) 8
(B) $f(x) = -x^2 + 1, x \in (-\infty, \infty)$	(II) 7
(C) $f(x) = x + 1, x \in [0, 6]$	(III) 1
(D) $f(x) = x^3, x \in [0, 2]$	(IV) 0

Choose the correct answer from the options given below :

2023: 30 May Shift 3

Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$

(A) Maximum value of $f(x)$ is 8

(B) Minimum value of $f(x)$ is 8

(D) No maximum value of $f(x)$

Choose the correct answer from the options given below :

If y=log⁡3(log⁡3x)y = \log_3(\log_3 x)y=log3​(log3​x), then dydx\frac{dy}{dx}dxdy​

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $y = \log_3(\log_3 x)$ , then $\frac{dy}{dx}$