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In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function ''f''(''x'', ''y'', ...) with respect to the variable ''x'' is variously denoted by : Since in general a partial derivative is a function of the same arguments as was the original function, this functional dependence is sometimes explicitly included in the notation, as in : The partial-derivative symbol is ∂. One of the first known uses of the symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences. The modern partial derivative notation is by Adrien-Marie Legendre (1786), though he later abandoned it; Carl Gustav Jacob Jacobi re-introduced the symbol in 1841. ==Introduction== Suppose that ''ƒ'' is a function of more than one variable. For instance, : . For the partial derivative at that leaves ''y'' constant, the corresponding tangent line is parallel to the ''xz''-plane. | image2 = X2+X+1.svg | caption2 = A slice of the graph above showing the function in the ''xz''-plane at . Note that the two axes are shown here with different scales. The slope of the tangent line is 3. }} The graph of this function defines a surface in Euclidean space. To every point on this surface, there are an infinite number of tangent lines. Partial differentiation is the act of choosing one of these lines and finding its slope. Usually, the lines of most interest are those that are parallel to the ''xz''-plane, and those that are parallel to the ''yz''-plane (which result from holding either y or x constant, respectively.) To find the slope of the line tangent to the function at P that is parallel to the ''xz''-plane, the ''y'' variable is treated as constant. The graph and this plane are shown on the right. On the graph below it, we see the way the function looks on the plane . By finding the derivative of the equation while assuming that ''y'' is a constant, the slope of ''ƒ'' at the point is found to be: : So at , by substitution, the slope is 3. Therefore : at the point . That is, the partial derivative of ''z'' with respect to ''x'' at is 3, as shown in the graph. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「partial derivative」の詳細全文を読む スポンサード リンク
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