grandes-ecoles 2019 Q4

grandes-ecoles · France · centrale-maths2__pc Implicit equations and differentiation Eliminate parameter from implicit family and derive ODE

Let $f$ be defined on $I = ]-\pi/2, \pi/2[$ by $f(x) = \frac{\sin x + 1}{\cos x}$. Show $$\forall x \in I, \quad 2f^{\prime}(x) = f(x)^2 + 1.$$

Let $f$ be defined on $I = ]-\pi/2, \pi/2[$ by $f(x) = \frac{\sin x + 1}{\cos x}$. Show
$$\forall x \in I, \quad 2f^{\prime}(x) = f(x)^2 + 1.$$