Найдите производную функции 1) f(x)=√x/(4+x) 2) f(x)=(2+√x)/(2-√x)

Question

Найдите производную функции
1) f(x)=√x/(4+x)
2) f(x)=(2+√x)/(2-√x)

Answer 1

F`(x)=[(√x)`*(4+x)-√x*(4+x)`]/(4=x)²=((4+x)/2√x -1*√x)/(4+x)²=
=(4+x-2x)/[2√x*(4+x)²]=(4-x)/[2√x)*(4+x)²]

f`(x)=[(2+√x)`*(2-√x)-(2+√x)*(2-√x)`]/(2-√x)²=[(2-√x)/2√x+(2+√x)/2√x]/(2-√x)²=
=(2-√x+2+√x)/[2√x(2-√x)²]=2/[√x(2-√x)²]