求大神导数求解==ln(x+根号下1+X的平方)‘的导数怎么解啊?我做的不对...

Question

求大神导数求解==ln(x+根号下1+X的平方)‘的导数怎么解啊?我做的不对...

Answer 1

导数={1/[x+√(x²+1)]}*[x+√(x²+1)]'
={1/[x+√(x²+1)]}*{1+[(x²+1)^(1/2)]'}
={1/[x+√(x²+1)]}*{1+(1/2)[(x²+1)^(-1/2)]*(x²+1)'}
={1/[x+√(x²+1)]}*{1+(1/2)[(x²+1)^(-1/2)]*2x}
={1/[x+√(x²+1)]}*[1+x/√(x²+1)]
={1/[x+√(x²+1)]}*[√(x²+1)+x]/√(x²+1)
=1/√(x²+1)

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