...*»(*), F'(y), F"(y) . ..... FW(y) ... (2). When we first find the partial differential coefficient of u with respect to x, and then with respect to y, the result has been repreHD c. 7 sented by F''(x, y) ; a notation which cannot conveniently be extended to the...

...equation is the second partial differential co-efficient of the function 'obtained by differentiating, first with respect to x, and then with respect to y ; the second member is the second partial differential co-efficient 18 which comes from differentiating,...

...special instances, differentiation with respect to x and y is commutative, or if one differentiates first with respect to x and then with respect to y, the result will be the same as if one proceeds in the opposite way, varying y first while holding x constant, then varying x while...

...Horner [ bipoly, {y, x} ] Out[8]= y (x (1 + 2x) +x (2 + 4x) y) Here the polynomial is put in Horner form first with respect to x and then with respect to y. The factorization that you obtain is dependent upon the ordering of the variables which you specify. In...

...derivative of /with respect to x / the second-order partial derivative of /obtained by differentiating first with respect to x and then with respect to y /"' the inverse of the function / the absolute value of z matrix with element Oy in the ¿th row and jth column...

...-.Y2y + G(y) where G and /i are arbitrary functions. To verify the solution, differentiate partially, first with respect to x and then with respect to y. The result is equation (4). Example 16 See § 1 2.6. We now carry out the reverse process to that of Example 13....