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设y=ln(x+根号(x^2+4),求d^2y/dx^2
题目详情
设y=ln(x+根号(x^2+4),求d^2y/dx^2
▼优质解答
答案和解析
所求就是y对x的二阶导数
y'=(x+根号(x^2+4))'/(x+根号(x^2+4))=(1+x/根号(x^2+4))/(x+根号(x^2+4))=1/根号(x^2+4)=(x^2+4)^(-1/2)
d^2y/dx^2=y''=（-1/2）*2x/(x^2+4)^(3/2)=-x（x^2+4）^(-3/2)
y'=(x+根号(x^2+4))'/(x+根号(x^2+4))=(1+x/根号(x^2+4))/(x+根号(x^2+4))=1/根号(x^2+4)=(x^2+4)^(-1/2)
d^2y/dx^2=y''=（-1/2）*2x/(x^2+4)^(3/2)=-x（x^2+4）^(-3/2)
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