If `x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2)` is `(varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^2)` (b) `(varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^3)` `varphi^(/)psi^` (d) `psi^(/)varphi^`

Options

A. `(phi'psi''-psi'phi'')/((phi')^(2))`
B. `(phi'psi''-psi'phi'')/((phi')^(3))`
C. `(phi'')/(psi'')`
D. `(psi'')/(phi'')`

Explanation

To find \( \frac{d^2y}{dx^2} \) given \( x = \varphi(t) \) and \( y = \psi(t) \), we will follow these steps:

### Step 1: Differentiate \( x \) and \( y \) with respect to \( t \)
We start by differentiating both \( x \) and \( y \):
\[ \frac{dx}{dt} = \varphi'(t) \]
\[
...