复合函数求导问题1)y=(3+x
1)y=(1+x)(1+x^2)^2
y'=(1+x)'(1+x^2)^2+(1+x)[(1+x)^2]'
=1*(1+x^2)^2+(1+x)*2*(1+x^2)*2x
=(1+x^2)[(1+x^2)+4x(1+x)]
=(1+x^2)(1+4x+5x^2)
2)y=log(3+2x^2)
y'=1/ln3**[2*2x/(3+2x^2)]
=4x/[(3+2x^2)ln3]
3)y=ln[tg(x/2)]
y'=1/tg(x/2)*1/[cos(x/2)]^2*1/2
=1/[2sin(x/2)cos(x/2)]
=1/sinx=cscx
4)y=[arcsin(x/3)]^5
y'...全部
1)y=(1+x)(1+x^2)^2
y'=(1+x)'(1+x^2)^2+(1+x)[(1+x)^2]'
=1*(1+x^2)^2+(1+x)*2*(1+x^2)*2x
=(1+x^2)[(1+x^2)+4x(1+x)]
=(1+x^2)(1+4x+5x^2)
2)y=log(3+2x^2)
y'=1/ln3**[2*2x/(3+2x^2)]
=4x/[(3+2x^2)ln3]
3)y=ln[tg(x/2)]
y'=1/tg(x/2)*1/[cos(x/2)]^2*1/2
=1/[2sin(x/2)cos(x/2)]
=1/sinx=cscx
4)y=[arcsin(x/3)]^5
y'=5*[arcsin(x/3)]^4*1/√[1-(x/3)^2]*1/3
=5/[arcsin(x/3)]^4/{3√[1-(x^2)/9]}
=5[arcsin(x/3)]^4/√(9-x^2)。
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