we know that when we try to expand a spring, we apply force, suppose F. we have seen that as we release the force the spring again get back to its opriginal position. it is because , there is a restoring force or spring force produced in thre spring when we apply force. it acts in ther opposite direction of the applied force.
and theis force is proportional to the expansion in the spring.
so we can write,
F=-kx this - sign comes because of the fact that displacement occurs in the opposite direction of this applied force.
and this k is constant for the spring . it depends on the stiffness of the spring.
and F =dV/dx