来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/08/19 17:55:58
求y=ln(a^2-x^2)的二阶导数
y=ln(a²-x²)
dy/dx=dln(a²-x²)/d(a²-x²)*d(a²-x²)/dx
=1/(a²-x²)*(-2x)
=-2x/(a²-x²)
d²y/dx²=-2*1/(a²-x²)²*[(a²-x²)*1-x*(-2x)]
=-2/(a²-x²)²*(a²-x²+2x²)
=-2/(a²-x²)²*(a²+x²)
=-2(a²+x²)/(a²-x²)²
=-1/(a+x)²-1/(a-x)²