<p>Degree of \\(\\left[1+\\left(\\dfrac{dy}{dx}\\right)^2\\right]^{3/2} = \\dfrac{d^2y}{dx^2}\\).</p>
Step-by-Step Solution
Key Concept: Integer/Numeric entry — compute exact numerical answer.
<div class='solution'><p>Square both sides to clear fractional power: $\left[1+(y')^2\right]^3 = (y'')^2$. Now a polynomial in derivatives. Highest derivative: $y''$, power: 2. <strong>Degree = 2</strong>.</p><p>⚠️ Trap: Saying degree = 3 from the LHS power before rationalising.</p></div>
Correct Answer: 2