Question

If x = t² and y = t³, find \[\frac{d^2 y}{d x^2}\] ?

Answer 1

Here,

\[x = t^2\text { and y } = t^3 \]
\[ \Rightarrow \frac{d x}{d t} = 2t \text { and } \frac{d y}{d t} = 3 t^2 \]
\[ \therefore \frac{d y}{d x} = \frac{3t}{2}\]
\[ \Rightarrow \frac{d^2 y}{d x^2} = \frac{3}{2}\frac{dt}{dx} = \frac{3}{4t}\]