f(x)=x+1/x
f'(x)=1-1/x^2=(x^2-1)/x^2
令f'(x)>0
x^2-1>0
x∈(负无穷,-1)∪(1,正无穷)时f(x)递增
f'(x)
f(x)=x+1/x的单调性和g（x)=x-1/x的单调性
0x^2-1>0x∈(负无穷,-1)∪(1,正无穷)时f(x)递增"}}}'>
f(x)=x+1/x
f'(x)=1-1/x^2=(x^2-1)/x^2
令f'(x)>0
x^2-1>0
x∈(负无穷,-1)∪(1,正无穷)时f(x)递增
f'(x)