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Re[1]: 偏微分の途中経過
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□投稿者/ X 大御所(310回)-(2008/12/08(Mon) 00:46:51)
 | (D/Dp){cosΦ(Df/Dp)-(sinΦ/p)(Df/DΦ)}cosΦ
+(D/DΦ){cosΦ(Df/Dp)-(sinΦ/p)(Df/DΦ)}(-sinΦ/p)
=(cosΦ)(D/Dp){cosΦ(Df/Dp)}
-(cosΦ)(D/Dp){(sinΦ/p)(Df/DΦ)}
+(-sinΦ/p)(D/DΦ){cosΦ(Df/Dp)}
-(-sinΦ/p)(D/DΦ){(sinΦ/p)(Df/DΦ)}
={(cosΦ)^2}(D^2f/Dp^2)}
-(cosΦ){(Df/DΦ)(D/Dp)(sinΦ/p)+(sinΦ/p)(D^2f/DpDΦ)}
+(-sinΦ/p){-sinΦ(Df/Dp)+cosΦ(D^2f/DΦDp)}
-(-sinΦ/p){(cosΦ/p)(Df/DΦ)+(sinΦ/p)(D^2f/DΦ^2)}
={(cosΦ)^2}(D^2f/Dp^2)}
-(cosΦ){-(Df/DΦ)(sinΦ/p^2)+(sinΦ/p)(D^2f/DpDΦ)}
+(-sinΦ/p){-sinΦ(Df/Dp)+cosΦ(D^2f/DpDΦ)}
-(-sinΦ/p){(cosΦ/p)(Df/DΦ)+(sinΦ/p)(D^2f/DΦ^2)}
={(cosΦ)^2}(D^2f/Dp^2)}
+(Df/DΦ)(sinΦcosΦ/p^2)-(sinΦcosΦ/p)(D^2f/DpDΦ)
+{(sinΦ)^2/p}(Df/Dp)-(sinΦcosΦ/p)(D^2f/DpDΦ)
+(sinΦcosΦ/p^2)(Df/DΦ)+{(sinΦ)^2/p^2}(D^2f/DΦ^2)
={(cosΦ)^2}(D^2f/Dp^2)}
+(Df/DΦ)(2sinΦcosΦ/p^2)-(2sinΦcosΦ/p)(D^2f/DpDΦ)
+{(sinΦ)^2/p}(Df/Dp)
+{(sinΦ)^2/p^2}(D^2f/DΦ^2)
となります。
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