求下列各函数的微分：

1）y=3x^2
y' = 6x

2) y=lnx^2

如果: y=ln(x^2)
令 x^2 = u
=>
y'
= (1/u)*u'
=1/(x^2)*2x
=2x/(x^2)
=2/x

如果: y=(lnx)^2
令 lnx = u
=>
y'
= 2*u*u'
= 2*lnx*(1/x)
= 2lnx/x
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5) y=e^(-x)cosx
令 u = e^(-x)
v = cosx
=>

y' = u'v + uv'
= -e^(-x)cosx - e^(-x)sinx
=-e^(-x)* (cosx + sinx)

7)y=ln√(1-x^3 )

令 u = √(1-x^3 )

y' = (1/u)*u'
= (1-x^3 )^(-1) * (1/2) * (1-x^3 )^(-0.5) * (-3) * x^2
= -(3/2)* (1-x^3)^(-3/2) * x^2

8)
y=tan(x/2)

令 x/2 = u
=>
y'= sec^2(x/2) * (1/2)
= (1/2) sec^2(x/2)

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若 y=(tanx)/2
=>
y'= (1/2)*sec^2(x)