If `x=asec^3theta,y=atan^3theta,` find `(d^2y)/(dx^2)` at `theta=pi/4`

Explanation

To find \(\frac{d^2y}{dx^2}\) at \(\theta = \frac{\pi}{4}\) given \(x = a \sec^3 \theta\) and \(y = a \tan^3 \theta\), we will follow these steps:

### Step 1: Differentiate \(x\) with respect to \(\theta\)
Given:
\[ x = a \sec^3 \theta \]
Using the chain rule, we differentiate:
...