CUET Preparation Today
If $x=at^2 $ and $y = a^3t^3 ,$ then $\frac{d^2y}{dx^2}$ will be : |
$\frac{3at}{2}$ $\frac{3}{4at}$ $\frac{3a}{4t}$ $\frac{3a^2t}{2}$ |
$\frac{3a}{4t}$ |
The correct answer is Option (3) → $\frac{3a}{4t}$ $\frac{dx}{dt}=2at$ $\frac{dy}{dt} = 3a^3t^2$ $\frac{dy}{dx}=\frac{3a^3t^2}{2at}=\frac{3a^2t}{2}$ $\frac{d^2y}{dx^2}=\frac{3a^2}{t}\frac{dt}{dx}=\frac{3a^2}{2×2at}=\frac{3a}{4t}$ |
