What is the derivative of $(\mathbf{u}(x))^TA\mathbf{v}(x)$ w.r.t. $x$?

Question

What is $\frac{d}{dx}(\mathbf{u}^TA\mathbf{v})$ where $\mathbf{u}$ and $\mathbf{v}$ are column-vector-valued functions of $x$, and $A$ is a matrix?

Is it $\frac{d\mathbf{u}^T}{dx}A\mathbf{v}+\mathbf{u}^TA\frac{d\mathbf{v}}{dx}$?

Answer 1

Yes, as @Hermis14 said, it's true.

Notice: it's based on hypothesis of "$A$ is a constant matrix".