Show that the slope of adiabatic curve at any point is `lamda` times the slope of an isothermal curve at the corresponding point.

Explanation

To show that the slope of the adiabatic curve at any point is \( \lambda \) times the slope of an isothermal curve at the corresponding point, we will start with the equations for both adiabatic and isothermal processes and differentiate them.

### Step-by-step Solution:

1. **Understand the Equations**:
- The equation for an adiabatic process is given by:
\[
PV^\gamma = \text{constant}
...