ln (e^x/(e^x+1))导数求解

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ln(e^x/(e^x+1))导数求解ln(e^x/(e^x+1))导数求解ln(e^x/(e^x+1))导数求解[ln(e^x/(e^x+1))]''=1/(e^x/(e^x+1))*(e^x/(e^

ln (e^x/(e^x+1))导数求解
ln (e^x/(e^x+1))导数求解

ln (e^x/(e^x+1))导数求解

[ln (e^x/(e^x+1))]'
=1/(e^x/(e^x+1)) *(e^x/(e^x+1))'
=(e^x+1)/e^x *[(e^x)'(e^x+1)-e^x(e^x+1)']/(e^x+1)^2
=(e^x+1)/e^x *(e^2x+e^x-e^2x)/(e^x+1)^2
=(e^x+1)/e^x *e^x/(e^x+1)^2
=1/(e^x...

全部展开

[ln (e^x/(e^x+1))]'
=1/(e^x/(e^x+1)) *(e^x/(e^x+1))'
=(e^x+1)/e^x *[(e^x)'(e^x+1)-e^x(e^x+1)']/(e^x+1)^2
=(e^x+1)/e^x *(e^2x+e^x-e^2x)/(e^x+1)^2
=(e^x+1)/e^x *e^x/(e^x+1)^2
=1/(e^x+1)

收起

f(x)=ln (e^x/(e^x+1))
f'(x)=(e^x+1)/(e^x)*[e^x(e^x+1)-e^2x]*e^x/(e^x+1)²
=e^x/(e^x+1)