能帮我求导一下:f(x)=ln(根号下x^2+1)吗,
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:2024/07/08 15:38:29
能帮我求导一下:f(x)=ln(根号下x^2+1)吗,
![能帮我求导一下:f(x)=ln(根号下x^2+1)吗,](/uploads/image/z/8620665-33-5.jpg?t=%E8%83%BD%E5%B8%AE%E6%88%91%E6%B1%82%E5%AF%BC%E4%B8%80%E4%B8%8B%EF%BC%9Af%28x%29%3Dln%28%E6%A0%B9%E5%8F%B7%E4%B8%8Bx%5E2%2B1%29%E5%90%97%2C)
f(x)=ln√(x²+1)
f'(x)=[1/√(x²+1)]*(√(x²+1))'
=[1/√(x²+1)]*[1/2√(x²+1)]*(x²+1)'
=[1/√(x²+1)]*[1/2√(x²+1)]*2x
=x/(x²+1)
f'(x)=[1/√(x²+1)]*(√(x²+1))'
=[1/√(x²+1)]*[1/2√(x²+1)]*(x²+1)'
=[1/√(x²+1)]*[1/2√(x²+1)]*2x
=x/(x²+1)