Let $A(x)=\left[\begin{array}{cc}x& 2\\ 3& 4\end{array}\right]$. Find $\frac{d}{dx}\det (A(x)).$

Step-by-step solution

1. Compute the determinant: det = x×4 − 2×3 = 4x − 6.
2. Differentiate with respect to x: d/dx(4x) = 4 and d/dx(−6) = 0.
3. Thus, $\frac{d}{dx}\det (A(x))=4$.

Concept tested: Derivative of determinant with variable

Published 3 September 2026 · How this solution was prepared and checked