Matrix-scalar chain rule

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$A(x)$ is a matrix-valued function, $x$ is a scalar, and $f(x)$ is a function that maps a scalar to another scalar.

Does that mean $\frac{\partial A(f(x))}{\partial x} = \frac{\partial A(f(x))}{\partial f(x)}\frac{\partial f(x)}{\partial x}$?