Find derivative of given function:

\(\displaystyle{D}'{\left({p}\right)}=^{{{1}}}{e}^{{{p}^{{{2}}}}}\dot{{{p}^{{{2}}}}}'+{5}\dot{{2}}{p}\)

\(\displaystyle={e}^{{{p}^{{{2}}}}}\dot{{2}}{p}+{10}{p}\)

\(\displaystyle={p}{\left({2}{e}^{{{p}^{{{2}}}}}+{10}\right)}\)

Rules used:

(1) Chain rule.

\(\displaystyle{D}'{\left({p}\right)}=^{{{1}}}{e}^{{{p}^{{{2}}}}}\dot{{{p}^{{{2}}}}}'+{5}\dot{{2}}{p}\)

\(\displaystyle={e}^{{{p}^{{{2}}}}}\dot{{2}}{p}+{10}{p}\)

\(\displaystyle={p}{\left({2}{e}^{{{p}^{{{2}}}}}+{10}\right)}\)

Rules used:

(1) Chain rule.