□投稿者/ X ファミリー(171回)-(2008/05/04(Sun) 14:02:01)
| これは又複雑ですね。 (間違っていたらごめんなさい。) (1) y'={(1/2)√[{1+x^(1/4)}/{1-x^(1/4)}]} ・[-{(1/4)/x^(3/4)}{1+x^(1/4)}-{(1/4)/x^(3/4)}{1-x^(1/4)}]/{1+x^(1/4)}^2 ={(1/2)√[{1+x^(1/4)}/{1-x^(1/4)}]}・{-(1/2)/x^(3/4)}/{1+x^(1/4)}^2 ={(-1/4)[{1+x^(1/4)}^(3/4)]/[{x^(3/4)}√{1-x^(1/4)}]
(2) y'=[(cosx)√{(acosx)^2+(bsinx)^2}-(sinx)(-a^2+b^2)(sinxcosx)/√{(acosx)^2+(bsinx)^2}]/{(acosx)^2+(bsinx)^2} =[(cosx){(acosx)^2+(bsinx)^2}-(sinx)(-a^2+b^2)(sinxcosx)] /{(acosx)^2+(bsinx)^2}^(3/2) =(cosx)[{(acosx)^2+(bsinx)^2}+(a^2-b^2)(sinx)^2] /{(acosx)^2+(bsinx)^2}^(3/2) ={(a^2)cosx}/{(acosx)^2+(bsinx)^2}^(3/2)
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