\( \left. \begin{array} { c } { f ( x ) = e ^ { x } \cdot x ^ { e } + \ln ( x ^ { 3 } + 1 ) ^ { \pi } = e ^ { x } \cdot x ^ { e } + \pi \cdot \ln ( x ^ { 3 } + 1 ) } \\ { f ^ { \prime } ( x ) = e ^ { x } \cdot x ^ { e } + e ^ { x } \cdot e \cdot x ^ { e - 1 } + \pi \cdot \frac { 3 x ^ { 2 } } { x ^ { 3 } + 1 } } \end{array} \right. \)

Find \( D_{x} y \) if \( y=\left(\frac{2}{x^{4}+1}+\frac{3}{x}\right) \)

\( \frac{d}{dx}(x^{2}+lnx-e^{3x)}) \)

9. Determinar la solución general del sistema: \[ \left\{\begin{array}{c}x_{1}^{\prime}=3 x_{1}+x_{2} \\ x_{2}^{\prime}=2 x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime}=2 x_{2}+3 x_{3}\end{array}\right. \]

Find an equation of the tangent plane to the given parametric surface at the specifie point. \( \begin{array}{l}\text { (a) } r(u, v)=\left(u^{2}+1\right) \mathbf{i}+\left(v^{3}+1\right) \mathbf{j}+(u+v) \mathbf{k} .(5,2,3) \\ \text { (b) } r(u, v)=\sin u \mathbf{i}+\cos u \sin v \mathbf{j}+\sin v \mathbf{k},(0.5, \sqrt{3} / 4,0.5)\end{array} \)

1. Calcula la siguiente integral definio \( \int_{0}^{\pi} \sin (x) d x \)