Step 1

\(\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}\)

Apply product rule for taking derivative

\(y=uv\)

\(y'=u'v+v'(u)\)

derivative of \(\displaystyle{\sin{{h}}}{\left({x}\right)}\ {i}{s}\ {\cos{{h}}}{\left({x}\right)}\)

Step 2

\(\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}\)

\(\displaystyle{y}'={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}+{e}^{{{x}}}{\cos{{h}}}{\left({x}\right)}\)

\(\displaystyle{y}'={e}^{{{x}}}{\left({\sin{{h}}}{\left({x}\right)}+{\cos{{h}}}{\left({x}\right)}\right)}\)