Final answer:
The x component of the electric field in a region with electric potential V(x) = 6/x is E(x) = -6/x^2.
Step-by-step explanation:
The x component of the electric field in a region can be found by taking the negative derivative of the electric potential V(x) with respect to x. In this case, V(x) = 6/x. To find the derivative, we use the power rule: dV/dx = -6/x^2. So, the x component of the electric field is E(x) = -6/x^2.
An example of this is if we have V(x) = 6/x, and we want to find the x component of the electric field at x = 2. Plugging this value into the equation, we get E(2) = -6/2^2 = -6/4 = -1.5.