x/根号下(a^2-x^2)的导数,参考学答案是a^2/(a^2-x^2)^(3/2)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/19 13:56:28
![x/根号下(a^2-x^2)的导数,参考学答案是a^2/(a^2-x^2)^(3/2)](/uploads/image/z/13957002-18-2.jpg?t=x%2F%E6%A0%B9%E5%8F%B7%E4%B8%8B%28a%5E2-x%5E2%29%E7%9A%84%E5%AF%BC%E6%95%B0%2C%E5%8F%82%E8%80%83%E5%AD%A6%E7%AD%94%E6%A1%88%E6%98%AFa%5E2%2F%28a%5E2-x%5E2%29%5E%283%2F2%29)
x/根号下(a^2-x^2)的导数,参考学答案是a^2/(a^2-x^2)^(3/2)
x/根号下(a^2-x^2)的导数,
参考学答案是a^2/(a^2-x^2)^(3/2)
x/根号下(a^2-x^2)的导数,参考学答案是a^2/(a^2-x^2)^(3/2)
复合函数的导数:
y’=1/根号下(a^2-x^2)
+x*{[(a^2-x^2)^(-1/2)]'}
[(a^2-x^2)^(-1/2)]'
=(-1/2)*[(a^2-x^2)^(-3/2)]*[(a^2-x^2)']
=x[(a^2-x^2)^(-3/2)]
所以
y’=1/根号下(a^2-x^2)
+(x^2)*[(a^2-x^2)^(-3/2)]
最后结果太繁琐,我不能确定我是否答对,所以不敢写上来,但可以肯定的是,LS的第一步就已经错了,所以结果也错
diff('x/sqrt(a^2-x^2)','x') =
1/(a^2-x^2)^(1/2)+x^2/(a^2-x^2)^(3/2)
过程其实很简单,就按求导的几种原则来做
原式
=1/(a^2-x^2)^(1/2) + x*(1/(a^2-x^2)^(1/2))'
(1/(a^2-x^2)^(1/2))'
=((a^2-x^2)^(-1/2))'...
全部展开
diff('x/sqrt(a^2-x^2)','x') =
1/(a^2-x^2)^(1/2)+x^2/(a^2-x^2)^(3/2)
过程其实很简单,就按求导的几种原则来做
原式
=1/(a^2-x^2)^(1/2) + x*(1/(a^2-x^2)^(1/2))'
(1/(a^2-x^2)^(1/2))'
=((a^2-x^2)^(-1/2))'
=-1/2*((a^2-x^2)^(-3/2))(a^2-x^2)'
=x*(a^2-x^2)^(-3/2)
原式
=1/(a^2-x^2)^(1/2)+x^2/(a^2-x^2)^(3/2)
1楼是正确的
再进行变形就可以了
=(a^2-x^2)/(a^2-x^2)^(3/2)+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)
收起
a