If y = x^( x), then value of x^(- x) dy/dx - x x is : Option 1: ( x)/x Option 2: x Option 3: x Option 4: ( x)/x

Answer: ( x)/x. Solution: Take log: y = x * x. Differentiate: 1/y dy/dx = x * x + ( x)/x. So dy/dx = x^( x) ( x * x + ( x)/x ). Multiplying by x^(- x): x^(- x) dy/dx = x * x + ( x)/x. Subtracting x x gives ( x)/x.

Calculus

Continuity & Differentiability

Medium

If $y = x^{\sin x}$ , then value of $x^{-\sin x} \frac{dy}{dx} - \cos x \log x$ is :

$\frac{\sin x}{x}$

$\sin x$

$\cos x$

$\frac{\cos x}{x}$

✅ Correct Option: 1

Take log: $\ln y = \sin x \cdot \ln x$ .

Differentiate: $\frac{1}{y} \frac{dy}{dx} = \cos x \cdot \ln x + \frac{\sin x}{x}$ .

So $\frac{dy}{dx} = x^{\sin x} \left( \cos x \cdot \log x + \frac{\sin x}{x} \right)$ .

Multiplying by $x^{-\sin x}$ : $x^{-\sin x} \frac{dy}{dx} = \cos x \cdot \log x + \frac{\sin x}{x}$ .

Subtracting $\cos x \log x$ gives $\frac{\sin x}{x}$ .

2025: 3 June Shift 1

Match List-I with List-II

List-I	List-II
Function	Points of discontinuity
(A) $f(x) = \frac{x^2 + 1}{x}$	(I) $x = 4$
(B) $f(x) = \frac{\vert x - 1 \vert}{x - 1}$	(II) $x = 2$
(C) $f(x) = \begin{cases} x - 1, & x < 2 \\ x + 1, & x \ge 2 \end{cases}$	(III) $x = 0$
(D) $f(x) = \frac{1 - x}{(x - 4)}$	(IV) $x = 1$

Choose the correct answer from the options given below:

2023: 23 May Shift 3

If $y = \sin^{-1}\left(\frac{1-x^2}{1+x^2}\right)$ then $\frac{dy}{dx} =$

2026: 18 May Shift 1

If $y = (1+x)(1+x^2)(1+x^4)$ , then $\frac{dy}{dx}$ at $x = -1$ is

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: 16 May Shift 1

If $y = (log x)^{(log x)}$ , $x > 1$ then $\frac{dy}{dx}$ is equal to

2026: 19 May Shift 2

For the function $f(x) = -2|\log_e|x||$ , which of the following is true?

If y=xsin⁡xy = x^{\sin x}y=xsinx, then value of x−sin⁡xdydx−cos⁡xlog⁡xx^{-\sin x} \frac{dy}{dx} - \cos x \log xx−sinxdxdy​−cosxlogx is :

Solution

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Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If $y = x^{\sin x}$ , then value of $x^{-\sin x} \frac{dy}{dx} - \cos x \log x$ is :