帮解几道求导的题,f(x)= (e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)

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帮解几道求导的题,f(x)= (e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)

帮解几道求导的题,f(x)= (e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)
帮解几道求导的题,
f(x)= (e^-5x)Cos3x
g(r)=r/根号(r^2+1)
x^2+y^2=2x^2y
y=e^(x/cosx)

帮解几道求导的题,f(x)= (e^-5x)Cos3xg(r)=r/根号(r^2+1)x^2+y^2=2x^2yy=e^(x/cosx)
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