If x = 6t^2, y = 6/t^2, then (d^2 y)/dx^2 is equal to : Option 1: -12 t^4 Option 2: 1/(3 t^6) Option 3: 1/(12 t^5) Option 4: -1/t^4

Answer: 1/(3 t^6). Solution: dx/dt = 12t, dy/dt = -12t^(-3). dy/dx = (-12t^(-3))/12t = -t^(-4). d^2y/dx^2 = d/dt(-t^(-4)) * 1/(dx/dt) = (4t^(-5))/12t = 1/3t^6.

Applied Mathematics

Calculus

Hard

applied

If $x = 6t^2$ , $y = \frac{6}{t^2}$ , then $\frac{d^2 y}{dx^2}$ is equal to :

$-12 t^4$

$\frac{1}{3 t^6}$

$\frac{1}{12 t^5}$

$-\frac{1}{t^4}$

✅ Correct Option: 2

$\frac{dx}{dt} = 12t$ , $\frac{dy}{dt} = -12t^{-3}$ . $\frac{dy}{dx} = \frac{-12t^{-3}}{12t} = -t^{-4}$ . $\frac{d^2y}{dx^2} = \frac{d}{dt}\left(-t^{-4}\right) \cdot \frac{1}{dx/dt} = \frac{4t^{-5}}{12t} = \frac{1}{3t^6}$ .

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If x=6t2x = 6t^2x=6t2, y=6t2y = \frac{6}{t^2}y=t26​, then d2ydx2\frac{d^2 y}{dx^2}dx2d2y​ is equal to :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $x = 6t^2$ , $y = \frac{6}{t^2}$ , then $\frac{d^2 y}{dx^2}$ is equal to :