Answer
$$A_c=m \\ A_h=\dfrac{q}{ 2} \\A_{k}=\dfrac{m}{q} \\A_{m}=\dfrac{k}{q}+c \\A_{q}=-\dfrac{km}{q^2}+\dfrac{h}{2}$$
Work Step by Step
Our aim is to take the first partial derivative of the given function $A$ with respect to one of its variables, by treating all others as a constant:
$$A_c=m \\ A_h=\dfrac{q}{ 2} \\A_{k}=\dfrac{m}{q} \\A_{m}=\dfrac{k}{q}+c \\A_{q}=-\dfrac{km}{q^2}+\dfrac{h}{2}$$
