Vector Derivative and Tangent – Calculating Derivative and a derivative size of a vector function – Exercise 3820 Post category:Vector Derivative and Tangent Post comments:0 Comments Exercise Given the vector function in the parametric presentation r⃗(t)=cos(2t)i⃗+sin(2t)j⃗+t2k⃗\vec{r}(t)=\cos (2t)\vec{i}+\sin (2t)\vec{j}+t^2\vec{k}r(t)=cos(2t)i+sin(2t)j+t2k Calculate dr⃗dt,∣dr⃗dt∣,d∣r∣⃗dt\frac{d\vec{r}}{dt},|\frac{d\vec{r}}{dt}|,\frac{d\vec{|r|}}{dt}dtdr,∣dtdr∣,dtd∣r∣ Final Answer Show final answer dr⃗dt=−2sin(2t)i⃗+2cos(2t)j⃗+2tk⃗\frac{d\vec{r}}{dt}=-2\sin (2t)\vec{i}+2\cos (2t)\vec{j}+2t\vec{k}dtdr=−2sin(2t)i+2cos(2t)j+2tk ∣dr⃗dt∣=21+t2|\frac{d\vec{r}}{dt}|=2\sqrt{1+t^2}∣dtdr∣=21+t2 d∣r∣⃗dt=2t31+t4\frac{d\vec{|r|}}{dt}=\frac{2t^3}{\sqrt{1+t^4}}dtd∣r∣=1+t42t3 Solution Coming soon… Share with Friends Read more articles Previous PostVector Derivative and Tangent – Calculating derivative of a vector function – Exercise 3825 You Might Also Like Vector Derivative and Tangent – Calculating derivative of a vector function – Exercise 3825 March 3, 2019 Vector Derivative and Tangent – A tangent calculation for a curve in a vector presentation – Exercise 3828 March 3, 2019 Vector Derivative and Tangent – A tangent calculation for a curve in a vector presentation – Exercise 3833 March 4, 2019 Vector Derivative and Tangent – A tangent calculation for a curve in a vector presentation – Exercise 3836 March 4, 2019 Vector Derivative and Tangent – Tangent to the curve in a vector representation parallel to a given plane – Exercise 3839 March 4, 2019 Vector Derivative and Tangent – Unit tangent vector to a curve in a vector presentation – Exercise 3842 March 4, 2019 Leave a Reply Cancel replyCommentEnter your name or username to comment Enter your email address to comment Enter your website URL (optional) Δ
Vector Derivative and Tangent – Calculating derivative of a vector function – Exercise 3825 March 3, 2019
Vector Derivative and Tangent – A tangent calculation for a curve in a vector presentation – Exercise 3828 March 3, 2019
Vector Derivative and Tangent – A tangent calculation for a curve in a vector presentation – Exercise 3833 March 4, 2019
Vector Derivative and Tangent – A tangent calculation for a curve in a vector presentation – Exercise 3836 March 4, 2019
Vector Derivative and Tangent – Tangent to the curve in a vector representation parallel to a given plane – Exercise 3839 March 4, 2019
Vector Derivative and Tangent – Unit tangent vector to a curve in a vector presentation – Exercise 3842 March 4, 2019