aufgabe 2b

$$f_2(x)=\sin \left(\frac{\cos x}{x}\right)$$

Ableitung §

$$\begin{array}{rl}{f}_2^{\prime }(x)& =\cos \left(\frac{\cos x}{x}\right)\cdot {\left(\frac{\cos x}{x}\right)}^{\prime }\\ & =\cos \left(\frac{\cos x}{x}\right)\cdot \frac{(\cos x{)}^{\prime }\cdot x-\cos x\cdot x^{\prime }}{x^2}\\ & =\cos \left(\frac{\cos x}{x}\right)\cdot \frac{-\sin x\cdot x-\cos x}{x^2}\\ & =-\cos \left(\frac{\cos x}{x}\right)\cdot \frac{\sin x}{x}-\frac{\cos x}{x^2}\end{array}$$