# Talk:Differential algebra

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Field:  Algebra

## elementary Leibniz differentials

I look in vain in wikipedia for an elementary explanation of the differential, (not the derivative). The Leibniz notations, ${\displaystyle {\frac {\mathrm {d} y}{\mathrm {d} x}}}$ and ${\displaystyle \int y\cdot dx,}$ assumes dx and dy. Formal differentiation can be defined: if x is a variable then so is dx, if x is constant then dx = 0, if x is an independent variable then dx is constant and d2x = 0, the sum rule d(x+y) = dx+dy, and the product rule d(x·y) = dx·y+dy. This is sufficient to deduce differentiation of formal power series. Differentiation of an algebraic equation (such as x2+y2 = r2) gives a differential equation (such as x·dx + y·dy = 0). Perhaps this is what this technical article on differential algebra is about ? Bo Jacoby 08:06, 7 August 2007 (UTC).