Question

y=x的平方+根号下【X-1/X+1】的导数怎么求啊

Answer 1

y=x²+√(x-1/x+1)=x²+(x-1/x+1)^½
y'=2x+1/2(x-1/x+1)^(1/2-1)*(x-1/x+1)'
=2x+1/2(x-1/x+1)^(-½)*(1+1/x²)
=2x+(1+1/x²)/2√(x-1/x+1)
前面的x²求导好求,后面的√(x-1/x+1)需要层层求导,先化成指数式(x-1/x+1)^½,然后要根据x^n的求导公式 {x^n的导数为nx^(n-1) } 代入,因为还没求到x的导数,还要对(x-1/x+1)再求导,(x-1/x+1)^½的导数为 1/2×(x-1/x+1)^(1/2-1)×(x-1/x+1)'=1/2×(x-1/x+1)^(-1/2)×(1+1/x²),这里-1/x 化成-x^(-1),还是根据x^n的求导公式,-x^(-1)‘=-1×(-1)x^(-1-1)=x^(-2)=1/x²