Question

If $x=t^2,y=t^3$ then $\frac{d^{2}y}{d{x}^2}=$

• A. $\frac{3}{2}$
• B. $\frac{3}{4t}$
• C. $\frac{3}{2t}$
• D. $\frac{3t}{2}$

Answer 1

The correct option is B $\frac{3}{4t}$

$x=t^2\Rightarrow \frac{dx}{dt}=2t$
$y=t^3\Rightarrow \frac{dy}{dt}={3t}^2$
$\Rightarrow \frac{dy}{dx}=\frac{{3t}^2}{2t}=\frac{3}{2}t$
$\therefore \frac{d^{2}y}{{dx}^2}=\frac{3}{2}\times \frac{dt}{dx}=\frac{3}{2}\times \frac{1}{2t}=\frac{3}{4t}$