\( f(x)=\frac{1}{\cos (x)}+\tan (x) \)
f(x)=\( \frac{1}{cos(x)} \)+\( \frac{sin(x)}{cos(x)} \)
f(x)=\( \frac{1+sin(x)}{cos(x)} \)
Nun mit der Quotientenregel:
\( f \cdot(x)=\frac{\cos (x) \cdot \cos (x)-(1+\sin (x)) \cdot(-\sin (x))}{\cos ^{2}(x)} \)
\( f \cdot(x)=\frac{\cos ^{2}(x)+(1+\sin (x)) \cdot(\sin (x))}{\cos ^{2}(x)} \)
\( f \cdot(x)=\frac{\cos ^{2}(x)+\sin (x)+\sin ^{2}(x)}{\cos ^{2}(x)}=\frac{1+\sin (x)}{\cos ^{2}(x)} \)