Question

425.Посчитайте $f'(a)$ при:
e)$f(x)=\frac{ln(x)}{2x},a=1$

Answer 1

$f(x)=\dfrac{lnx}{2x}\ \ ,\ \ a=1\\\\\\y'=\dfrac{\dfrac{1}{x}\cdot 2x-2\cdot lnx}{4x^2}=\dfrac{2\cdot (1-lnx)}{4x^2}\\\\\\a=1\ \ ,\ \ f'(1)=\dfrac{2\cdot (1-ln1)}{4}=\dfrac{2}{4}=\dfrac{1}{2}$