Vector Derivative and Tangent – Calculating Derivative and a derivative size of a vector function – Exercise 3820

Exercise

Given the vector function in the parametric presentation

r(t)=cos(2t)i+sin(2t)j+t2k\vec{r}(t)=\cos (2t)\vec{i}+\sin (2t)\vec{j}+t^2\vec{k}

Calculate

drdt,drdt,drdt\frac{d\vec{r}}{dt},|\frac{d\vec{r}}{dt}|,\frac{d\vec{|r|}}{dt}

Final Answer

drdt=2sin(2t)i+2cos(2t)j+2tk\frac{d\vec{r}}{dt}=-2\sin (2t)\vec{i}+2\cos (2t)\vec{j}+2t\vec{k}

drdt=21+t2|\frac{d\vec{r}}{dt}|=2\sqrt{1+t^2}

drdt=2t31+t4\frac{d\vec{|r|}}{dt}=\frac{2t^3}{\sqrt{1+t^4}}

Solution

Coming soon…

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