$\begin{array}{l}
j)y' = \sqrt {\sin \left( {{e^{2x}} + {x^2}} \right)} '\\
= \frac{{\left( {\sin \left( {{e^{2x}} + {x^2}} \right)} \right)'}}{{2\sqrt {\sin \left( {{e^{2x}} + {x^2}} \right)} }} = \frac{{\left( {{e^{2x}} + {x^2}} \right)'.\cos \left( {{e^{2x}} + {x^2}} \right)}}{{2\sqrt {\sin \left( {{e^{2x}} + {x^2}} \right)} }}\\
= \frac{{\left( {2{e^{2x}} + 2x} \right)\cos \left( {{e^{2x}} + {x^2}} \right)}}{{2\sqrt {\sin \left( {{e^{2x}} + {x^2}} \right)} }} = \frac{{\left( {{2^{2x}} + x} \right)\cos \left( {{e^{2x}} + {x^2}} \right)}}{{\sqrt {\sin \left( {{e^{2x}} + {x^2}} \right)} }}
\end{array}$
