If x=t^3, y=t^4, then d^2y/dx^2 is: Option 1: 4/3 Option 2: 4/3t Option 3: 4/3t^2 Option 4: 4/9t^2

Answer: 4/9t^2. Solution: dy/dx=4t^3/3t^2=4t/3. Then d^2y/dx^2=d/dt(4t/3)/dt=(4/3)/3t^2=4/9t^2.

Calculus

Continuity & Differentiability

Medium

core

If $x=t^3, y=t^4$ , then $\frac{d^2y}{dx^2}$ is:

$\frac{4}{3}$

$\frac{4}{3t}$

$\frac{4}{3t^2}$

$\frac{4}{9t^2}$

✅ Correct Option: 4

$\frac{dy}{dx}=\frac{4t^3}{3t^2}=\frac{4t}{3}$ .

Then $\frac{d^2y}{dx^2}=\frac{d}{dt}\left(\frac{4t}{3}\right)\div\frac{dx}{dt}=\frac{4/3}{3t^2}=\frac{4}{9t^2}$ .

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