f(x)= (e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)这4道题不大会做,麻烦帮解下,感激不尽!

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f(x)=(e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)这4道题不大会做,麻烦帮解下,感激不尽!f(x)=(e^-5x)Cos3xg(r)=

f(x)= (e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)这4道题不大会做,麻烦帮解下,感激不尽!
f(x)= (e^-5x)Cos3x
g(r)=r/根号(r^2+1)
x^2+y^2=2x^2y
y=e^(x/cosx)
这4道题不大会做,麻烦帮解下,感激不尽!

f(x)= (e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)这4道题不大会做,麻烦帮解下,感激不尽!
郭敦顒回答:
(1)f(x)= (e^-5x)Cos3x
f′(x)=[ (e^-5x)Cos3x] ′=(e^-5x) ′Cos3x+(e^-5x)(Cos3x)′
=-5(e^-5x)Cos3x-3(e^-5x)sin3x=-(e^-5x)(5 cos3 x+3 sin3 x)
(2)g(r)=r/根号(r^2+1)
g′(r)=[ r/√(r^2+1)] ′={ r′√(r^2+1) -r [√(r^2+1)] ′}/[√(r^2+1)] ²
={√(r^2+1) -r [1/2×2 r]}/ (r^2+1)=[ √(r^2+1) -r ²]/(r^2+1)
(3)x^2+y^2=2x^2y
两边对x求导,2 x+2 y(y)′=4xy(2y)′=8xy(y)′
∴8xy(y)′-2 y(y)′=2x
y′=x/(4xy-y)
(4)y=e^(x/cosx)
y′=[ e^(x/cosx) ] ′= e^(x/cosx)•[x/cosx] ′
∵[x/cosx] ′= [x′cosx-xcos′x]/ cos ² x=(cosx+ xsinx)/cos ² x
∴y′= e^(x/cosx)• (cosx+ xsinx)/cos ² x

1.积法则
=(e^-5x)'cos3x+e^-5x(cos3x)'
=e^-5x(-5)cos3x+e^-5x(-sin3x)(3)
=e^-5x(-5cos3x-3sin3x)
2.商法则
={r'根号(r^2+1)-r[根号(r^2+1)]'}/(根号(r^2+1))^2
=[根号(r^2+1)-r^2/根号(r^2+1)]/(r^2+1)

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1.积法则
=(e^-5x)'cos3x+e^-5x(cos3x)'
=e^-5x(-5)cos3x+e^-5x(-sin3x)(3)
=e^-5x(-5cos3x-3sin3x)
2.商法则
={r'根号(r^2+1)-r[根号(r^2+1)]'}/(根号(r^2+1))^2
=[根号(r^2+1)-r^2/根号(r^2+1)]/(r^2+1)
3.两边对x求导
2x+2y*y'=4xy+2x^2y'
y'=(4xy-2x)/(2y-2x^2)
=(2xy-x)/(y-x^2)
4.链式
y'=e^(x/cosx)(x/cosx)'
=e^(x/cosx)(x'cosx-x(cosx'))/cos^2 x
=e^(x/cosx)(cosx+xsinx)/cos^2 x

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