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The greatest common factor of 12xy2 + 6x is 6x. The greatest common factor of 12 and 6 is 6, and the greatest common factor of xy2 and x is x. If you took 6x out of both factors, the end result would be 2y2+1
4xy4xy 12xy2*2xy 2*2*3xy4xy(1+/-3)
-5xy2 + 12xy2 = (-5 + 12)xy2 = 7xy2
The derivative with respect to 'x' is 4y3 . The derivative with respect to 'y' is 12xy2 .