Question

Найдите производную функции

Answer 1

19. f'(x) = $frac{(sqrt{x})'*(4+x)- sqrt{x}*(4+x)' }{(4+x)^2}= frac{frac{4+x}{2sqrt{x}} -  sqrt{x} }{(4+x)^2} =  frac{4+x-2x}{2 sqrt{x}(4+x)^2} =  frac{4-x}{2sqrt{x}(x+4)^2}$

20. f'(x) =$frac{(2+sqrt{x})'(2-sqrt{x})-(2-sqrt{x})'(2+sqrt{x})}{(2-sqrt{x})^2} = frac{frac{2-sqrt{x}}{2sqrt{x}}-frac{2+sqrt{x}}{-2sqrt{x}} }  {(2-sqrt{x})^2} =  frac{2-sqrt(x)+2+sqrt{x}}{2sqrt{x}(2-sqrt{x})^2} = frac{2}{(2-sqrt{x})^2sqrt{x}}$

21.-