Производные [latex] y=(log_{2}(\sqrt{x}+1))^{5} [/latex]

[latex]y'=5(log_{2}( \sqrt{x} +1))^4* \frac{1}{( \sqrt{x} +1)ln2}* \frac{1}{2 \sqrt{x} }= \\ \\ = \frac{5(log_{2}( \sqrt{x} +1))^4}{(x+ \sqrt{x} )ln2^2}= \frac{5(log_{2}( \sqrt{x} +1))^4}{(x+ \sqrt{x} )ln4} [/latex]