ln[x+√(1+x2)] 的导数怎么解?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/26 05:09:46
ln[x+√(1+x2)] 的导数怎么解?
错了 是这个 ln[x+√(1+x^2)]
错了 是这个 ln[x+√(1+x^2)]
![ln[x+√(1+x2)] 的导数怎么解?](/uploads/image/z/3350667-3-7.jpg?t=ln%5Bx%2B%E2%88%9A%281%2Bx2%29%5D+%E7%9A%84%E5%AF%BC%E6%95%B0%E6%80%8E%E4%B9%88%E8%A7%A3%3F)
(ln[x+√(1+x²)])'
=[x+√(1+x²)]'/[x+√(1+x²)]
=[1+1/2*2x/√(1+x²)]/[x+√(1+x²)]
=[1+x/√(1+x²)]/[x+√(1+x²)]
=[x+√(1+x²)]/{[x+√(1+x²)]*√﹙1+x²)}
=1/√﹙1+x²)
=[x+√(1+x²)]'/[x+√(1+x²)]
=[1+1/2*2x/√(1+x²)]/[x+√(1+x²)]
=[1+x/√(1+x²)]/[x+√(1+x²)]
=[x+√(1+x²)]/{[x+√(1+x²)]*√﹙1+x²)}
=1/√﹙1+x²)