What is the degree of $\left(1 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = \frac{d^2y}{dx^2}$?

Explanation

1. 01

   First clear the fractional power by squaring: $\left(1 + \left(\frac{dy}{dx}\right)^2\right)^3 = \left(\frac{d^2y}{dx^2}\right)^2$.

2. 02

   Now the highest derivative, $\frac{d^2y}{dx^2}$, is to the power 2: the degree is 2.