证明函数y=ln(1+1/x)在(0,正无穷)上单调递减

问题描述:

证明函数y=ln(1+1/x)在(0,正无穷)上单调递减

y' = (1 + 1/x)(-1/x²) = -(x + 1)/x³
x > 0,x³ > 0,x + 1 > 0,y' = -(x + 1)/x³