The sum of the order and the degree of the differential equation $\frac{d}{dx} \left( \left( \frac{dy}{dx} \right)^3 \right)$ is:

3

The correct answer is Option (2) → 3 ##

The given differential equation is $\frac{d}{dx} \left( \left( \frac{dy}{dx} \right)^3 \right)$.

Differentiate the given equation = $3 \left( \frac{dy}{dx} \right)^2 \frac{d^2y}{dx^2}$

Thus, the order and degree of the differential equation is 2 and 1 respectively. The sum of the order and the degree is $2 + 1 = 3$.