Aufgabe:
Ich habe folgende Frage. Ich versteh alles bis zum blau markierten. Wieso wird dann allerdings die Ableitung genutzt? 
Text erkannt:
(1) \( \Sigma F_{x}: F_{R_{0}}+G \sin \alpha_{1}-F \cos \alpha_{2}=0 \)
(2) \( \sum F_{y}: F_{N}+F_{\sin \alpha_{2}}-G \cos \alpha_{1}=0 \)
(3) \( F_{R_{0}}=\mu_{0} F_{N} \)
(9) \( F_{x_{0}}=F_{\cos \alpha_{2}}-G_{\sin \alpha_{1}} \)
(2) \( F_{N}=G_{\cos \alpha} \alpha_{1}-F_{\sin \alpha_{2}} \)
\( x^{4} \frac{x}{x} \)
(9)=(3) \( F \cos \alpha_{2}-G \sin \alpha_{1}=\mu_{0}\left(G \cos \alpha_{1}-F \sin \alpha_{2}\right) \)
\( F \cos \alpha_{2}+\mu_{0} F_{\sin \alpha_{2}}=\mu_{0} G \cos \alpha_{1}+G \sin \alpha_{1} \)
\( F\left(\cos \alpha_{2}+\mu_{0} \sin \alpha_{2}\right)=G\left(\sin \alpha_{1}+\mu_{0} \cos \alpha_{1}\right) \)
\( F=\frac{G\left(\sin \alpha_{1}+\mu_{0} \cos \alpha_{1}\right)}{\cos \alpha_{2}+\mu_{0} \sin \alpha_{2}} \)
\( F^{\prime}=\frac{d F}{d \alpha_{2}}=\frac{0-G\left(\sin \alpha_{1}+\mu_{0} \cos \alpha_{1}\right)\left(-\sin \alpha_{2}+\mu_{0} \cos \alpha_{2}\right)}{\left(\cos \alpha_{2}+\mu_{0} \sin \alpha_{2}\right)^{2}} \)
\( F^{\prime}=0 \)
\( \rightarrow \theta=-\sin \alpha_{2}+\mu_{0} \cos \alpha_{2} \)
\( \sin \alpha_{2}=\mu_{0} \cos \alpha_{2} \)
\( \frac{\sin \alpha_{2}}{\cos \alpha_{2}}=\mu_{0} \)
\( \tan \alpha_{2}=\mu_{0} \)
mit \( \mu_{0}=\tan \rho_{0} \rightarrow \tan \alpha_{2}=\tan \rho_{0} \rightarrow \underline{\underline{\alpha_{2}}=\rho_{0}} \)
