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If $x=6t,y=4t^3,$ then the value of $\frac{d^2y}{dx^2}$ is : |
$\frac{3}{2}t $ $\frac{4}{5t}$ $\frac{4}{3t}$ $\frac{2}{3}t$ |
$\frac{2}{3}t$ |
The correct answer is Option (4) → $\frac{2}{3}t$ $x=6t$, $\frac{dx}{dt}=6$ $y=4t^3$, $\frac{dy}{dt}=12t^2$ $⇒\frac{dy}{dx}=\frac{12t^2}{6}=2t^2$ $⇒\frac{d^2y}{dx^2}=4t×\frac{dt}{dx}=4t×\frac{1}{6}$ $=\frac{2}{3}t$
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