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d/dc (a_1 * b_1^2 + a_2 * c^2 + a_3 * d_3^2) / (b^2 + c^2 + d^2)
d/dc (a_1 * b_1^2 + a_2 * c^2 + a_3 * d_3^2) / (b^2 + c^2 + d^2)
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