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Let \( f(x)=x+(1-x) x^{2}+(1-x)\left(1-x^{2}\right) x^{3}+\ldots \ldots+(1-x)\left(1-x^{2}\right) \ldots \ldots\left(1-x^{n-1}\right) x^{n} ;(n \geq 4) \) then :
\( \mathrm{P} \)
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(a) \( f(x)=-\prod_{r=1}^{n}\left(1-x^{r}\right) \)
(b) \( f(x)=1-\prod_{r=1}^{n}\left(1-x^{r}\right) \)
(c) \( f^{\prime}(x)=(1-f(x))\left(\sum_{r=1}^{n} \frac{r x^{r-1}}{\left(1-x^{r}\right)}\right) \)
(d) \( f^{\prime}(x)=f(x)\left(\sum_{r=1}^{n} \frac{r x^{r-1}}{\left(1-x^{r}\right)}\right) \)
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