Find the derivative of the function given by $f(x) =( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)$ and hence find $ f' (1).$

Question

$\begin{array}{1 1} ( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)\bigg(\large\frac{1}{1+x}+\frac{2x}{1+x^2}+\frac{4x^{\Large 3}}{1-x^{\Large 4}}+\large\frac{8x^{\Large7}}{1-x^{\large 8}}\bigg) , f'(1)=60 \\ ( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)\bigg(\large\frac{1}{1+x}+\frac{2x}{1-x^2}+\frac{4x^{\Large 3}}{1+x^{\Large 4}}+\large\frac{7x^{\Large7}}{1+x^{\large 8}}\bigg) , f'(1)=120\\ \bigg(\large\frac{1}{1+x}+\frac{2x}{1+x^2}+\frac{4x^{\Large 3}}{1+x^{\Large 4}}+\large\frac{8x^{\Large7}}{1+x^{\large 8}}\bigg) , f'(1)=240 \\ ( 1 + x )( 1 + x^2) ( 1 + x^4) ( 1 + x^8)\bigg(\large\frac{1}{1+x}+\frac{2x}{1+x^2}+\frac{4x^{\Large 3}}{1+x^{\Large 4}}+\large\frac{8x^{\Large7}}{1+x^{\large 8}}\bigg) , f'(1)=120\end{array} $