Question
Write the value of $\frac{\text{d}}{\text{dx}}(\text{x}|\text{x}|)$
$\frac{\text{d}}{\text{dx}}(\text{x}|\text{x}|)=\begin{cases}\frac{\text{d}}{\text{dx}}\text{x}^2&\big[\text{if }\text{x}>0\big]\\\frac{\text{d}}{\text{dx}}(-\text{x})\text{x}&\big[\text{if }\text{x}<0\big]\end{cases}$
$=\begin{cases}\text{2x}&[\text{if }\text{x}>0]\\-\text{2x}&[\text{if }\text{x}<0]\end{cases}$
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Find the number of terms in the expansion of $(\text{a}+\text{b}+\text{c})^{\text{n}}.$
If
$(1-\text{x}+\text{x}^{2})^{\text{n}}=\text{a}^{0}+\text{a}_{1}\text{x}+\text{a}_{2}\text{x}^{2}+...+\text{a}_{2\text{n}}\text{x}^{2\text{n}},$find the value of $\text{a}_{0}+\text{a}_{2}+\text{a}_{4}+...+\text{a}_{2\text{n}}.$A multiple of 2 or 3.