求函数y=ln(arctantx+1/x-1)的导数
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y =ln(arctan[(x+1)/(x-1)] )
y' = (1/arctan[(x+1)/(x-1)]) .d/dx (arctan[(x+1)/(x-1)])
=(1/arctan[(x+1)/(x-1)]) .1/{ 1+[(x+1)/(x-1)]^2 } .d/dx [(x+1)/(x-1)]
=(1/arctan[(x+1)/(x-1)]) .1/{ 1+[(x+1)/(x-1)]^2 } .[-2/(x-1)^2]
=(1/arctan[(x+1)/(x-1)]) .(x-1)^2/(2(x^2+1)) .[-2/(x-1)^2]
=-1/ { (x^2+1).artan[(x+1)/(x-1)] }
y' = (1/arctan[(x+1)/(x-1)]) .d/dx (arctan[(x+1)/(x-1)])
=(1/arctan[(x+1)/(x-1)]) .1/{ 1+[(x+1)/(x-1)]^2 } .d/dx [(x+1)/(x-1)]
=(1/arctan[(x+1)/(x-1)]) .1/{ 1+[(x+1)/(x-1)]^2 } .[-2/(x-1)^2]
=(1/arctan[(x+1)/(x-1)]) .(x-1)^2/(2(x^2+1)) .[-2/(x-1)^2]
=-1/ { (x^2+1).artan[(x+1)/(x-1)] }
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