求导:y=ln(x+√(a^2+x^2))i need process and detailed steps if necessary.

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 03:54:28
求导:y=ln(x+√(a^2+x^2))ineedprocessanddetailedstepsifnecessary.求导:y=ln(x+√(a^2+x^2))ineedprocessanddet

求导:y=ln(x+√(a^2+x^2))i need process and detailed steps if necessary.
求导:y=ln(x+√(a^2+x^2))
i need process and detailed steps if necessary.

求导:y=ln(x+√(a^2+x^2))i need process and detailed steps if necessary.
y'=[1/(x+√(a^2+x^2))]*[x+√(a^2+x^2)]'
=[1/(x+√(a^2+x^2))]*[1+2x/2√(a^2+x^2)]
=[1/(x+√(a^2+x^2))]*[(√(a^2+x^2)+x)/√(a^2+x^2)]
=1/√(a^2+x^2)

y'={1/[x+√(a²+x²)]}*[x+√(a²+x²)]'
={1/[x+√(a²+x²)]}*[1+1/2√(a²+x²)*(a²+x²)']
={1/[x+√(a²+x²)]}*[1+2x/2√(a²+x²)]
={1/[x...

全部展开

y'={1/[x+√(a²+x²)]}*[x+√(a²+x²)]'
={1/[x+√(a²+x²)]}*[1+1/2√(a²+x²)*(a²+x²)']
={1/[x+√(a²+x²)]}*[1+2x/2√(a²+x²)]
={1/[x+√(a²+x²)]}*[1+x/√(a²+x²)]
={1/[x+√(a²+x²)]}*{[√(a²+x²)+x]/√(a²+x²)}
=1/√(a²+x²)

收起