If x = at^2 and y = a^3 t^3, then (d^2 y)/dx^2 will be : Option 1: 3at/2 Option 2: 3/4at Option 3: 3a/4t Option 4: (3a^2 t)/2

Answer: 3a/4t. Solution: dx/dt = 2at, dy/dt = 3a^3 t^2. dy/dx = (3a^3 t^2)/2at = (3a^2 t)/2. d^2y/dx^2 = d/dt(dy/dx) * dt/dx = 3a^2/2 * 1/2at = 3a/4t. Note: Treating y = a^3 t^3 literally with cubic in a; if intended as y = at^3, the answer would differ.

Applied Mathematics

Calculus

Medium

If $x = at^2$ and $y = a^3 t^3$ , then $\frac{d^2 y}{dx^2}$ will be :

$\frac{3at}{2}$

$\frac{3}{4at}$

$\frac{3a}{4t}$

$\frac{3a^2 t}{2}$

✅ Correct Option: 3

$\frac{dx}{dt} = 2at$ , $\frac{dy}{dt} = 3a^3 t^2$ .

$\frac{dy}{dx} = \frac{3a^3 t^2}{2at} = \frac{3a^2 t}{2}$ .

$\frac{d^2y}{dx^2} = \frac{d}{dt}\left(\frac{dy}{dx}\right) \cdot \frac{dt}{dx} = \frac{3a^2}{2} \cdot \frac{1}{2at} = \frac{3a}{4t}$ .

Note: Treating $y = a^3 t^3$ literally with cubic in a; if intended as $y = at^3$ , the answer would differ.

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If $y = x^3 \log x$ , then $\frac{d^2 y}{dx^2}$ is equal to :

If x=at2x = at^2x=at2 and y=a3t3y = a^3 t^3y=a3t3, then d2ydx2\frac{d^2 y}{dx^2}dx2d2y​ will be :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $x = at^2$ and $y = a^3 t^3$ , then $\frac{d^2 y}{dx^2}$ will be :