diff --git a/Mathe.pdf b/Mathe.pdf index 9e944dd..925bffe 100644 Binary files a/Mathe.pdf and b/Mathe.pdf differ diff --git a/Mathe_11_2.tex b/Mathe_11_2.tex index b12509a..5f5c03d 100644 --- a/Mathe_11_2.tex +++ b/Mathe_11_2.tex @@ -829,7 +829,7 @@ \subsubsection{Produktregel} \begin{gather*} k(x) = f(x) \cdot g(x) \\ k'(x) = \lim\limits_{h \to 0} \frac{f(x + h) \cdot g(x + h) - f(x) \cdot g(x)}{h} \\ - \;= \lim\limits_{h \to 0} \frac{f(x + h) \cdot g(x + h) {\color{red}- f(x \cdot g(x + h) + f(x) \cdot g(x + h)} - f(x) \cdot g(x)}{h} \\ + \;= \lim\limits_{h \to 0} \frac{f(x + h) \cdot g(x + h) {\color{red}- f(x) \cdot g(x + h) + f(x) \cdot g(x + h)} - f(x) \cdot g(x)}{h} \\ \;= \lim\limits_{h \to 0} \frac{{\color{blue}[f(x + h) - f(x)]} \cdot g(x + h) + f(x) \cdot {\color{violet}[g(x + h) - g(x)]}}{h} \\ \;= \boldsymbol{{\color{blue}f'(x)} \cdot g(x) + f(x) \cdot {\color{violet}g'(x)}} \end{gather*}