Aus Online Mathematik Brückenkurs 2

By using the rule for differentiation

\displaystyle \frac{d}{dx}\,x^{n}=nx^{n-1}

and the fact that the expression can be differentiated term by term and that constant factors can be taken outside the differentiation, we obtain

\displaystyle \begin{align} f^{\,\prime}(x) &= \frac{d}{dx}\,\bigl(x^2-3x+1\bigr)\\[5pt] &= \frac{d}{dx}\,x^2 - 3\frac{d}{dx}\,x^1 + \frac{d}{dx}\,1\\[5pt] &= 2x^{2-1} - 3\cdot 1x^{1-1} + 0\\[5pt] &= 2x-3\,\textrm{.} \end{align}