Question

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

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

Answer 1

Answer: (B)

$x=t^2\dots \left(i\right)$,
$y=t^3\dots \left(ii\right)$
From $(i)$ and $(ii)$, we get $y=x^{3/2}$
Differentiating w.r.t. to $x$, we get
$\frac{dy}{dx}=\frac{3}{2}{x}^{\frac{1}{2}}$
Again differentiating w.r.t. to $x$, we get
$\frac{d^{2}y}{d{x}^2}=\frac{3}{4\sqrt{x}}=\frac{3}{4t}$ (from eqn. $(i)$)