prove that the curl of the gradient of F(scalar function)is zero
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Since each component of F is a derivative of f, we can rewrite the curl as curl∇f=(∂2f∂y∂z−∂2f∂z∂y,∂2f∂z∂x−∂2f∂x∂z,∂2f∂x∂y−∂2f∂y∂x). ... If f is twice continuously differentiable, then its second derivatives are independent of the order in which the derivatives are applied.
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