If y = _e (x^3/e^3), then (d^2 y)/(d x^2) is equal to Option 1: -1/x^2 Option 2: 1/x^2 Option 3: -3/x^2 Option 4: 3/x^2

Answer: -3/x^2. Solution: y = _e(x^3) - _e(e^3) = 3_e x - 3. So dy/dx = 3/x and d^2y/dx^2 = -3/x^2.

Applied Mathematics

Calculus

Easy

applied

If $y = \log_e \left(\frac{x^3}{e^3}\right)$ , then $\frac{d^2 y}{d x^2}$ is equal to

$-\frac{1}{x^2}$

$\frac{1}{x^2}$

$-\frac{3}{x^2}$

$\frac{3}{x^2}$

✅ Correct Option: 3

$y = \log_e(x^3) - \log_e(e^3) = 3\log_e x - 3$ . So $\frac{dy}{dx} = \frac{3}{x}$ and $\frac{d^2y}{dx^2} = -\frac{3}{x^2}$ .

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 :

2026: 14 May Shift 2

If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$

2023: 23 May Shift 3

The total cost of producing $x$ generators is given by

TC = $x^3 - 60x^2 + 1500x + 2000$ .

The Marginal Cost (MC), when $x = 10$ units is:

2026: 21 May Shift 2

Given that the total cost function for x units of a commodity is $C(x) = \dfrac{x^3}{4} + 4x^2 - 8x + 20$ . Then the marginal cost when $x=4$ is:

2023: 23 May Shift 3

If $y = \frac{\log x}{x^2}$ , then $\frac{d^2y}{dx^2}$ is equal to

2023: 7 June Shift 1

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

If y=log⁡e(x3e3)y = \log_e \left(\frac{x^3}{e^3}\right)y=loge​(e3x3​), then d2ydx2\frac{d^2 y}{d x^2}dx2d2y​ is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $y = \log_e \left(\frac{x^3}{e^3}\right)$ , then $\frac{d^2 y}{d x^2}$ is equal to