If y = [x^2/e^2] then value of d^2y/dx^2 is : Option 1: x^2/e^4 Option 2: (-2)/x^2 Option 3: e/x^2 Option 4: 2x + 2

Answer: (-2)/x^2. Solution: y = (x^2/e^2) = 2 x - 2. dy/dx = 2/x. d^2y/dx^2 = -2/x^2.

Calculus

Continuity & Differentiability

Easy

common

If $y = \log\left[\frac{x^2}{e^2}\right]$ then value of $\frac{d^2y}{dx^2}$ is :

$\frac{x^2}{e^4}$

$\frac{-2}{x^2}$

$\frac{e}{x^2}$

$2x + \log 2$

✅ Correct Option: 2

$y = \log\left(\frac{x^2}{e^2}\right) = 2\log x - 2$ .

$\frac{dy}{dx} = \frac{2}{x}$ .

$\frac{d^2y}{dx^2} = -\frac{2}{x^2}$ .

2025: 14 May Shift 2

If $y = x\sin y$ , then $\frac{dy}{dx}$ is:

2026: 15 May Shift 1

The graph of a function $f: R \to R$ is shown below, where $R$ is a real numbers

Then which of following statements is correct?

2025: 21 May Shift 2

Differentiation of $\log[\log(\log x^5)]$ with respect to $x$ is

2026: 14 May Shift 2

If $y=\frac{\log x}{x}$ , then $\frac{d^2y}{dx^2}$ is equal to(Consider $\log_e x = \log x$ ):

2023: 23 May Shift 3

If $y = x^x$ , $\frac{dy}{dx}$ will be:

2026: 22 May Shift 2

If $y=\tan^{-1}(x+y)$ , then $\frac{d^2y}{dx^2}$ is equal to: