Let \( y=e^{x} \ln x \), then \( y^{\prime}= \)

Application 3: Simplifier les expressions suivantes: \( \begin{array}{ll}A=\ln (\sqrt{3})+\ln 3-\ln 9 & ; \\ C=\ln \left(\frac{1}{3}\right)+\ln \left(\frac{3}{5}\right)+\ln \left(\frac{5}{7}\right)+\ln \left(\frac{7}{9}\right) & ;\end{array} \quad D=\ln (\sqrt[3]{2}-\ln 16 \)

Find the derivative of the function. \[ y=\frac{7}{x^{4}}-\frac{2}{x} \]

Determine the first derivative of the \( 1.1 \quad y=x^{3}-\cot \left(x^{3}+3 x-1\right) \)

Calcula el área entre las curvas \( y = x^3 - 3x \) y \( y = x + 1 \) sobre el intervalo definido por sus intersecciones.

A solid is formed with triangular cross-sections where each triangle's base is defined by the equation \(y = x^2\) on interval \([0, 2]\). What is the volume of this solid?