# Vector Derivative and Tangent – Calculating derivative of a vector function – Exercise 3825

Exercise

Given the vector function in the parametric presentation

$$\vec{r}(t)=\frac{1}{2}\tan^4(2t)\vec{i}-t\cos(3t)\vec{j}+\ln(4t)\vec{k}$$

Calculate its derivative.

$$\vec{r}'(t)=\frac{4\tan^3(2t)}{\cos^2(2t)}\vec{i}+(3t\sin (3t)-\cos (3t))\vec{j}+\frac{1}{t}\vec{k}$$