Calcular \( y^{\prime}=\frac{d y}{d x} \) de la función implicita \( \frac{x^{2}}{4}+\frac{x^{2}}{9}=3 x y \) y simplificar:

Encuentre el centroide de la región acotada por las curvas: \( y=2 x-4, y=2 \sqrt{x}, x=1 \)

Find the value. \[ \begin{array}{l}\operatorname{In}\left(\frac{92}{20}\right) \\ \text { In }\left(\frac{92}{20}\right) \approx \square \\ \text { (Round the final answer to four decimal places as needed. Round }\end{array} \]

Encontrar \( f(t) \) si \( F(s)=\frac{2}{(s+2)^{4}}+\frac{3}{s^{2}+16}+\frac{5(s+1)}{s^{2}+2 s+5} \)

Given the system of differential equations: \[ \frac{d \mathbf{x}}{d t}=A \mathbf{x} \] where \( A=\left(\begin{array}{ll}4 & 0 \\ 0 & 3\end{array}\right) \), what is the general solution for \( \mathbf{x}(t) \) ?

\( \int \frac { \operatorname { cen } x d x } { \cos x ( \cos x - 1 ) } \)