x= at² এবং y=2at

  $\frac{d^{2} y}{dx^{2}}$   কোনটি?  

$\begin{array}{l}x=a t^{2} \Rightarrow \quad y=2 a t \\ \frac{d y}{d x}=\frac{2 a}{2 a t} \\ \Rightarrow \quad \frac{d^{2} y}{d x^{2}}=-\frac{1}{t^{2}} \frac{d t}{d x} \\ \Rightarrow \quad-\frac{1}{t^{2}} \cdot \frac{1}{2 a t}=-\frac{1}{2 a t^{3}}\end{array}$

$\begin{array}{l}x=a t^{2} \Rightarrow \quad y=2 a t \\ \frac{d y}{d x}=\frac{2 a}{2 a t} \\ \Rightarrow \quad \frac{d^{2} y}{d x^{2}}=-\frac{1}{t^{2}} \frac{d t}{d x} \\ \Rightarrow \quad-\frac{1}{t^{2}} \cdot \frac{1}{2 a t}=-\frac{1}{2 a t^{3}}\end{array}$