\( y = \ln \quad | \sec 2 x ^ { 3 } | \)

Determine the implied domain of the following function. Express your answer in interval notation.

On considère la fonction numérique \( f \) définie par: \[ f(x)=x-\sqrt{3-x^{2}} \] 1. Determiner \( D f \). \( \forall x \in D_{f} \quad f(x) \geq-2 \sqrt{3} \). 2. Montrer que : \( -2 \sqrt{3} \) est - il la valeur minimale de \( f \) sur \( D_{f} \).

Derivative DF \( F(x)=\frac{x}{\sqrt[3]{x^{2}+4}} \)

Differentiate. (Hint: Use the Extended Power Rule.) \( g(x)=(\ln x)^{4} \)

Find the general form of \( f \) if \( f^{\prime}(x)=8 f(x) \).