\(f(x) = \frac1{\sqrt{2x +5}}\)
\(f(x+h) = \frac1{\sqrt{2(x+ h) +5}}\)
\(f'(x) = \lim\limits_{h\to 0} \frac{f(x+h)-f(x)}h\)
\(= \lim\limits_{h \to 0} \cfrac{\frac1{\sqrt{2(x+h)+5}}-\frac 1{\sqrt{2x+5}}}{h}\)
\(= \lim\limits_{h \to 0}\frac{\sqrt{2x+5} - \sqrt{2(x+h)+5}}{h\sqrt{2(x+h)+5}\sqrt{2x + 5}}\)
\(= \lim\limits_{h \to 0} \frac{(2x + 5) - (2x + 2h+5)}{h\left(\sqrt{2(x+h)+5} + \sqrt{2x+5}\right) \sqrt{2x +5}\sqrt{2x + 2h + 5}}\)
\(= \lim\limits_{h \to 0} \frac{-2}{2(2x + 5)^{3/2}}\)
\(= \frac{-1}{(2x + 5)^{3/2}}\)
