Question

Найдите производную функции

Answer 1

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

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

21.-