Use symbolic toolbox. First define the equation
syms alpha b q r x_1 x_2 x_3
eq = alpha*x_1 + b*x_2 + q*abs(x_2)*x_2 + r*x_3;
and take derivative w.r.t to different variables
>> diff(eq, x_1) % derivative w.r.t x_1
ans =
alpha
>> diff(eq, x_2) % derivative w.r.t x_2
ans =
b + q*abs(x_2) + q*x_2*sign(x_2)
>> diff(eq, x_3) % derivative w.r.t x_3
ans =
r
