求这个函数的导数 5
2个回答
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-(4/3)x/(x⁴-1)
解：
(1) 变换形式
f(x)
=(1/3)ln[(x²+1)/(x²-1)]
=(1/3)[ln(x²+1)-ln(x²-1)]
=(1/3)(A-B)
(2) 分项求导
A'
=[ln(x²+1)]'
=[1/(x²+1)]*(x²+1)'
=2x/(x²+1)
B'
=[ln(x²-1)]'
=[1/(x²-1)]*(x²-1)'
=2x/(x²-1)
(3) 汇总
f'(x)
=(1/3)*[2x/(x²+1)-2x/(x²-1)]
=(1/3)*2x[1/(x²+1)-1/(x²-1)]
=-(4/3)x/(x⁴-1)
解：
(1) 变换形式
f(x)
=(1/3)ln[(x²+1)/(x²-1)]
=(1/3)[ln(x²+1)-ln(x²-1)]
=(1/3)(A-B)
(2) 分项求导
A'
=[ln(x²+1)]'
=[1/(x²+1)]*(x²+1)'
=2x/(x²+1)
B'
=[ln(x²-1)]'
=[1/(x²-1)]*(x²-1)'
=2x/(x²-1)
(3) 汇总
f'(x)
=(1/3)*[2x/(x²+1)-2x/(x²-1)]
=(1/3)*2x[1/(x²+1)-1/(x²-1)]
=-(4/3)x/(x⁴-1)
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