28.15. Compute the derivative of the function $f(x)=\cos ^{x} a - \sin ^{x} a$, where $0<a<\pi / 2$ is a constant angle.

## 28.3. Multiple root of a polynomial
28.15. According to problem 28.13

$f^{\prime}(x)=\cos ^{x} a \cdot \ln \cos a-\sin ^{x} a \cdot \ln \sin a=\cos ^{x} a\left(\ln \cos a-\operatorname{tg}^{x} a \cdot \ln \sin a\right)$.