Given f(x)=7x2+5x+1\displaystyle {f{{\left({x}\right)}}}={7}{x}^{{2}}+{5}{x}+{1}, find f(x)\displaystyle {f}'{\left({x}\right)} using the limit definition of the derivative.

f(x)\displaystyle {f}'{\left({x}\right)}=  

Note: You must show your work, and you must use the limit definition for the derivative for full credit.