The given function can be decomposed into two functions, the outer function will be,

\(\displaystyle{g{{\left({h}\right)}}}={71}{e}^{{h}}\)

and the inner function will be,

\(\displaystyle{h}{\left({x}\right)}={0.2}{x}\)

so when we compose these function we get the composite function,

\(\displaystyle{f{{\left({x}\right)}}}={g}{o}{h}{\left({x}\right)}={71}{e}^{{{0.2}{x}}}\)

The formula for differentiation of composite function is,

\(\displaystyle{f}′{\left({x}\right)}={g}′{\left({h}{\left({x}\right)}\right)}·{h}′{\left({x}\right)}\)

substitute \(\displaystyle{g{{\left({h}\right)}}}={71}{e}^{{h}}\) and \(\displaystyle{h}{\left({x}\right)}={0.2}{x}\) into the formula,

\(\displaystyle{f}'{\left({x}\right)}=\frac{{d}}{{{d}{h}{\left({x}\right)}}}{\left({71}{e}^{{{h}{\left({x}\right)}}}\right)}\cdot\frac{{x}}{{\left.{d}{x}\right.}}{\left({0.2}{x}\right)}\)

\(\displaystyle={71}{e}^{{{h}{\left({x}\right)}}}\cdot{0.2}\)

\(\displaystyle={14.2}{e}^{{{0.2}{x}}}\)

hence the differentiation of f(x) is \(\displaystyle{14.2}{e}^{{{0.2}{x}}}.\)

\(\displaystyle{g{{\left({h}\right)}}}={71}{e}^{{h}}\)

and the inner function will be,

\(\displaystyle{h}{\left({x}\right)}={0.2}{x}\)

so when we compose these function we get the composite function,

\(\displaystyle{f{{\left({x}\right)}}}={g}{o}{h}{\left({x}\right)}={71}{e}^{{{0.2}{x}}}\)

The formula for differentiation of composite function is,

\(\displaystyle{f}′{\left({x}\right)}={g}′{\left({h}{\left({x}\right)}\right)}·{h}′{\left({x}\right)}\)

substitute \(\displaystyle{g{{\left({h}\right)}}}={71}{e}^{{h}}\) and \(\displaystyle{h}{\left({x}\right)}={0.2}{x}\) into the formula,

\(\displaystyle{f}'{\left({x}\right)}=\frac{{d}}{{{d}{h}{\left({x}\right)}}}{\left({71}{e}^{{{h}{\left({x}\right)}}}\right)}\cdot\frac{{x}}{{\left.{d}{x}\right.}}{\left({0.2}{x}\right)}\)

\(\displaystyle={71}{e}^{{{h}{\left({x}\right)}}}\cdot{0.2}\)

\(\displaystyle={14.2}{e}^{{{0.2}{x}}}\)

hence the differentiation of f(x) is \(\displaystyle{14.2}{e}^{{{0.2}{x}}}.\)