Answer
\[\frac{{dy}}{{dx}} = \cos x + 2{e^{0.5x}}\]
Work Step by Step
\[\begin{gathered}
y = \sin x + 4{e^{0.5x}} \hfill \\
\hfill \\
differentiate \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \,\,{\left[ {\sin x} \right]^,} + \,\,{\left[ {4{e^{0.5x}}} \right]^,} \hfill \\
\frac{{dy}}{{dx}} = \,\,{\left[ {\sin x} \right]^,} + \,\,4{\left[ {{e^{0.5x}}} \right]^,} \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \cos x + 4\,\left( {0.5} \right){e^{0.5x}} \hfill \\
\hfill \\
multiply \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \cos x + 2{e^{0.5x}} \hfill \\
\hfill \\
\end{gathered} \]
