Question

帮解几道求导的题，谢谢！！

f(x)= (e^-5x)Cos3x
g(r)=r/根号（r^2+1)
x^2+y^2=2x^2y
y=e^(x/cosx)

Answer 1

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

追问

谢谢，我等下算算对不对，回来给您分