${f}'(x)=1\times \frac{f(x)}{x}+2\times \frac{f(x)}{2x+1}+3\times \frac{f(x)}{3x+2}+...+51\times \frac{f(x)}{51x+50}\Rightarrow {f}'(-1)=1+2+3+...+51=\frac{51\times 52}{2}=1326$