函数y=ln(1-x)除以(1+x),则y''(0)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/26 16:35:14
函数y=ln(1-x)除以(1+x),则y''''(0)函数y=ln(1-x)除以(1+x),则y''''(0)函数y=ln(1-x)除以(1+x),则y''''(0)y=(1+x)⁻¹ln

函数y=ln(1-x)除以(1+x),则y''(0)
函数y=ln(1-x)除以(1+x),则y''(0)

函数y=ln(1-x)除以(1+x),则y''(0)
y = (1+x)⁻¹ln(1-x)
y' = (-1)(1+x)⁻²ln(1-x) + (1+x)⁻¹ (1-x)⁻¹(-1)
= -(1+x)⁻²ln(1-x) - (1-x²)⁻¹
y'' = -(-2)(1+x)⁻³ln(1-x) - (1+x)⁻²(1-x)⁻¹(-1) - (-1)(1-x²)⁻²(-2x)
= 2(1+x)⁻³ln(1-x) + (1+x)⁻²(1-x)⁻¹ -2x(1-x²)⁻²
x = 0,y'' = 2(1+0)⁻³ln(1-0) + (1+0)⁻²(1-0)⁻¹ -2*0)(1-0²)⁻²
= 0 + 1+ 0
= 1