1) \( \frac{d}{d x} 3\left(2 x^{3}-6\right)^{4}= \)

Ex. \[ \text { Let } f(x)=13 x-6 . \text { Find } f^{\prime}(\mathbf{4}) \]

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

Evaluate the line integral \( \int_{C} \mathbf{F} \cdot d \mathbf{r} \), where \( \mathbf{F}(x, y, z)=5 \sin (x) \mathbf{i}-4 \cos (y) \mathbf{j}-2 x z \mathbf{k} \) and C is given by the vector function \( \mathbf{r}(t)=t^{5} \mathbf{i}-t^{4} \mathbf{j}+t^{3} \mathbf{k}, \quad 0 \leq t \leq 1 \).

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

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