大一微积分 求导数求函数y=√{1+tan[x+(1/x)]}的导数书上是这么解的:y'={√[1+tan(1+1/x)]}'=1/2{√[1+tan(1+1/x)]}^(-1/2)乘以[1+tan(x+1/x)]'注意看乘以二次前的那部分:1/2{√[1+tan(1+1/x)]}^(-1/2)为什么根号没
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![大一微积分 求导数求函数y=√{1+tan[x+(1/x)]}的导数书上是这么解的:y'={√[1+tan(1+1/x)]}'=1/2{√[1+tan(1+1/x)]}^(-1/2)乘以[1+tan(x+1/x)]'注意看乘以二次前的那部分:1/2{√[1+tan(1+1/x)]}^(-1/2)为什么根号没](/uploads/image/z/7207143-15-3.jpg?t=%E5%A4%A7%E4%B8%80%E5%BE%AE%E7%A7%AF%E5%88%86+%E6%B1%82%E5%AF%BC%E6%95%B0%E6%B1%82%E5%87%BD%E6%95%B0y%3D%E2%88%9A%7B1%2Btan%5Bx%2B%281%2Fx%29%5D%7D%E7%9A%84%E5%AF%BC%E6%95%B0%E4%B9%A6%E4%B8%8A%E6%98%AF%E8%BF%99%E4%B9%88%E8%A7%A3%E7%9A%84%EF%BC%9Ay%27%3D%7B%E2%88%9A%5B1%2Btan%281%2B1%2Fx%29%5D%7D%27%3D1%2F2%7B%E2%88%9A%5B1%2Btan%281%2B1%2Fx%29%5D%7D%5E%28-1%2F2%29%E4%B9%98%E4%BB%A5%5B1%2Btan%28x%2B1%2Fx%29%5D%27%E6%B3%A8%E6%84%8F%E7%9C%8B%E4%B9%98%E4%BB%A5%E4%BA%8C%E6%AC%A1%E5%89%8D%E7%9A%84%E9%82%A3%E9%83%A8%E5%88%86%EF%BC%9A1%2F2%7B%E2%88%9A%5B1%2Btan%281%2B1%2Fx%29%5D%7D%5E%28-1%2F2%29%E4%B8%BA%E4%BB%80%E4%B9%88%E6%A0%B9%E5%8F%B7%E6%B2%A1)
大一微积分 求导数求函数y=√{1+tan[x+(1/x)]}的导数书上是这么解的:y'={√[1+tan(1+1/x)]}'=1/2{√[1+tan(1+1/x)]}^(-1/2)乘以[1+tan(x+1/x)]'注意看乘以二次前的那部分:1/2{√[1+tan(1+1/x)]}^(-1/2)为什么根号没
大一微积分 求导数
求函数y=√{1+tan[x+(1/x)]}的导数
书上是这么解的:y'={√[1+tan(1+1/x)]}'=1/2{√[1+tan(1+1/x)]}^(-1/2)乘以[1+tan(x+1/x)]'
注意看乘以二次前的那部分:1/2{√[1+tan(1+1/x)]}^(-1/2)为什么根号没去掉?根号就是1/2次幂 根据(x^a)'=ax^(a-1)公式变成了1/2和-1/2次幂了吗?那为啥根号还在呢?
大一微积分 求导数求函数y=√{1+tan[x+(1/x)]}的导数书上是这么解的:y'={√[1+tan(1+1/x)]}'=1/2{√[1+tan(1+1/x)]}^(-1/2)乘以[1+tan(x+1/x)]'注意看乘以二次前的那部分:1/2{√[1+tan(1+1/x)]}^(-1/2)为什么根号没
点击放大、再点击再放大:
一级一级的求就好了。就是一楼的那样了,sec后面的在分子上。
(tan x)’=sec x×sec x
y=√{1+tan[x+(1/x)]}
y'= 1/2 *1/√{1+tan[x+(1/x)]} * {1+tan[x+(1/x)]}'
= 1/2 *1/√{1+tan[x+(1/x)]} * {sec[x+(1/x)]}^2 * [x+1/x]'
= 1/2 *1/√{1+tan[x+(1/x)]} * {sec[x+(1/x)]}^2 * [1-1/x^2]