(a) Differentiate $A(m,h)$ with respect to $m$ to find $A_m(m,h)$.
$$A_m(m,h)=\frac{\partial }{\partial m}\left(0.024265h^{0.3964}{m}^{0.5378}\right)=$$
(Round to five decimal places as needed.)

Step 1 ：Differentiate the function $A(m,h)=0.024265h^{0.3964}{m}^{0.5378}$ with respect to $m$ using the power rule for differentiation.

Step 2 ：The power rule states that the derivative of $x^n$ with respect to $x$ is $n\ast x^{n-1}$.

Step 3 ：In this case, we need to differentiate $0.024265\ast h^{0.3964}\ast m^{0.5378}$ with respect to $m$.

Step 4 ：The derivative of a product of functions is given by the product rule, which states that the derivative of $f(x)\ast g(x)$ is $f^{\prime }(x)\ast g(x)+f(x)\ast g^{\prime }(x)$.

Step 5 ：Here, $f(m)=m^{0.5378}$ and $g(m)=0.024265\ast h^{0.3964}$. So, we need to find $f^{\prime }(m)$ and $g^{\prime }(m)$ and then use the product rule to find the derivative of the function.

Step 6 ：The derivative of $A(m,h)$ with respect to $m$ is $A_m(m,h)=0.013049717h^{0.3964}{m}^{-0.4622}$.

Step 7 ：$\boxed{{\displaystyle A_m(m,h)=0.013049717h^{0.3964}{m}^{-0.4622}}}$