Express the derivatives $f^{\prime}, f^{\prime\prime}$ and $f^{(3)}$ using usual functions, where $f$ is defined on $I = ]-\pi/2, \pi/2[$ by $$\forall x \in I, \quad f(x) = \frac{\sin x + 1}{\cos x}.$$
Express the derivatives $f^{\prime}, f^{\prime\prime}$ and $f^{(3)}$ using usual functions, where $f$ is defined on $I = ]-\pi/2, \pi/2[$ by
$$\forall x \in I, \quad f(x) = \frac{\sin x + 1}{\cos x}.$$