Question

Найдите производную функции
y=(1/x)+2lnx-(lnx/x)

Answer 1

(x^n)'=n*x^(n-1)
(ln x )'=1/x
(u/v)'=(u' *v - v'*u)/v^2
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y=(1/x)+2lnx-(lnx/x)
(1/x)'=(x^-1)'=-1 * x^-2=-1/x^2
(lnx)'=1/x
(lnx/x)'=(lnx'*x - x' * lnx)/x^2=(1/x*x- 1 *lnx)/x^2=(1-lnx)/x^2
y=-1/x^2+2x/x^2-(1-lnx)/x^2= (lnx + 2x - 2)/x^2