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- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/07%3A_Work_and_Energy/7.15%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/08%3A_Work_and_Energy/8.15%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/09%3A_Work_Power_and_Energy/9.09%3A_Conservative_and_Non-Conservative_ForcesIf the derivative of the y-component of the force with respect to x is equal to the derivative of the x-component of the force with respect to y, the force is a conservative force, which means the pat...If the derivative of the y-component of the force with respect to x is equal to the derivative of the x-component of the force with respect to y, the force is a conservative force, which means the path taken for potential energy or work calculations always yields the same results.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/09%3A_Potential_Energy_and_Conservation_of_Energy/9.03%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/08%3A_Potential_Energy_and_Conservation_of_Energy/8.03%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Workbench/PH_245_Textbook_V2/04%3A_Module_3_-_Conservation_Laws/4.01%3A_Objective_3.a./4.1.07%3A_Conservative_and_Non-Conservative_ForcesA conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for whi...A conservative force is one for which the work done is independent of path. Equivalently, a force is conservative if the work done over any closed path is zero. A non-conservative force is one for which the work done depends on the path. The component of a conservative force, in a particular direction, equals the negative of the derivative of the potential energy for that force, with respect to a displacement in that direction.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Heat_and_Thermodynamics_(Tatum)/02%3A_Partial_Derivatives/2.05%3A_Second_Derivatives_and_Exact_DifferentialsIf z=z(x,y), we can go through the motions of calculating ∂z∂x and ∂z∂y, and we can then further calculate the second derivatives \(...If z=z(x,y), we can go through the motions of calculating ∂z∂x and ∂z∂y, and we can then further calculate the second derivatives ∂2z∂x2, ∂2x∂y2, ∂2z∂y∂x and ∂2z∂y∂x.
