高数y=(a^2-x^2)^1⼀2的二阶导数,谢谢

2025-01-19 17:13:52
推荐回答(1个)
回答1:

二阶导数计算如下:
y'=(1/2)*(a^2-x^2)^(-1/2)*(-2x)
=-x*(a^2-x^2)^(-1/2)
y''=-(a^2-x^2)^(-1/2)-x*(-1/2)*(a^2-x^2)^(-3/2)*(-2x)
=-(a^2-x^2)^(-1/2)-x^2(a^2-x^2)^(-3/2)
=-(a^2-x^2+x^2)*(a^2-x^2)^(-3/2)
=-a^2*(a^2-x^2)^(-3/2)