Question

Can someone derivate this??

Answer 1

I guess you mean "differentiate". Just differentiate each component:

`\vec r(t)=t^2\,\vec\imath-\vec\jmath+2(t+1)\,\vec k`

`\implies(\mathrm d\vec r(t))/(\mathrm dt)=(\mathrm d[t^2])/(\mathrm dt)\,\vec\imath+(\mathrm d[-1])/(\mathrm dt)\,\vec\jmath+(\mathrm d[2(t+1)])/(\mathrm dt)\,\vec k`

`(\mathrm d\vec r(t))/(\mathrm dt)=2t\,\vec\imath+2\,\vec k`