If $x=6t^2, y = \frac{6}{t^2}, $ then $\frac{d^2y}{dx^2}$ is equal to :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{1}{3\, t^6}$
$\frac{dy}{dt}=\frac{-12}{t^3},\frac{dx}{dt}=12t$
$∴\frac{dy}{dx}=\frac{-12}{t^3×12t}=\frac{-1}{t^4}$
$⇒\frac{d^2y}{dx^2}=\frac{t^4}{t^5}×\frac{1}{12t}$ $[\frac{dt}{dx}=\frac{1}{12t}]$
$=\frac{1}{3t^6}$