# Vector Derivative and Tangent – A tangent calculation for a curve in a vector presentation – Exercise 3828

Exercise

Calculate the tangent equation for the curve

$$\vec{r}(t)=.(te^{-t}+3)\vec{i}+\sqrt{4+5t}\vec{j}+\arctan(2t)\vec{k}$$

At a point corresponding to t = 0.

$$\vec{x}=(1,\frac{5}{4},2)t+(3,2,0)$$