A curve is represented parametrically by the equations `x=f(t)=a^(In(b^t))and y=g(t)=b^(-In(a^(t)))a,bgt0 and a ne 1, b ne 1" Where "t in R.`
The value of `(d^(2)y)/(dx^(2))` at the point where f(t)=g(t) is

Options

A. 0
B. `(1)/(2)`
C. 1
D. 2

Explanation

To solve the problem, we need to find the value of \(\frac{d^2y}{dx^2}\) at the point where \(f(t) = g(t)\). Let's break down the solution step by step.

### Step 1: Define the Parametric Equations
We start with the given parametric equations:
\[ x = f(t) = a^{\ln(b^t)} = a^{t \ln b} \]
\[
...