Question

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

 

Options

• 3/2

• 3/4t

• 3/2t

• 3t/2

Answer 1

(b) 3/4t

Here,

\[x = t^2 \text { and y }= t^3 \]

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

\[ \therefore \frac{d y}{d x} = \frac{3t}{2}\]

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