Find derivative of given function:

\(\displaystyle{y}'=^{{{1}}}{\left({5}{x}^{{{3}}}\right)}'+{\left({7}{x}^{{{2}}}\right)}'-{\left({3}{x}\right)}'+{1}'\)

\(\displaystyle=^{{{2}}}{5}\dot{{3}}{x}^{{{2}}}+{7}\dot{{2}}{x}-{3}\dot{{1}}+{0}\)

\(\displaystyle={15}{x}^{{{2}}}+{14}{x}-{3}\)

Rules used:

(1) Derivative of sum

(2) Power rule

\(\displaystyle{y}'=^{{{1}}}{\left({5}{x}^{{{3}}}\right)}'+{\left({7}{x}^{{{2}}}\right)}'-{\left({3}{x}\right)}'+{1}'\)

\(\displaystyle=^{{{2}}}{5}\dot{{3}}{x}^{{{2}}}+{7}\dot{{2}}{x}-{3}\dot{{1}}+{0}\)

\(\displaystyle={15}{x}^{{{2}}}+{14}{x}-{3}\)

Rules used:

(1) Derivative of sum

(2) Power rule