Find the derivative of the vector function. r(t)=a+tb+t^2c

trainart1 2021-11-13 Answered
Find the derivative of the vector function. \(\displaystyle{r}{\left({t}\right)}={a}+{t}{b}+{t}^{{2}}{c}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Charles Randolph
Answered 2021-11-14 Author has 1561 answers
\(\displaystyle{r}{\left({t}\right)}={a}+{t}{b}+{t}^{{2}}{c}\)
a,b,c are any constant vectors, like i, j, k, but not necessarily pointing in the same directions or having the same magnitudes.
Take the derivative of whatever is multiplying each vector, as usual.
\(\displaystyle{r}'{\left({t}\right)}={\left({1}\right)}'{a}+{\left({t}\right)}'{b}+{\left({t}^{{2}}\right)}'{c}\)
\(\displaystyle={\left({0}\right)}{a}+{\left({1}\right)}{b}+{\left({2}{t}\right)}{c}\)
\(\displaystyle={b}+{2}{t}{c}\)
Result: \(\displaystyle{r}'{\left({t}\right)}={K}+{2}{t}{c}\)
Have a similar question?
Ask An Expert
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-28
Find the domain of the vector function.
\(\displaystyle{r}{\left({t}\right)}={t}-\frac{{2}}{{t}}+{2}{i}+{\sin{{t}}}{j}+{\ln{{\left({9}-{t}^{{2}}\right)}}}{k}\)
asked 2021-09-16
The curvature given by the vector function r is
\(\displaystyle{k}{\left({t}\right)}={\frac{{{\left|{r}'{\left({t}\right)}\times{r}{''}{\left({t}\right)}\right|}}}{{{\left|{r}'{\left({t}\right)}\right|}^{{{3}}}}}}\)
Use the formula to find the curvature of \(\displaystyle{r}{\left({t}\right)}={\left\langle\sqrt{{{15}{t}}},\ {e}^{{{t}}},\ {e}^{{-{t}}}\right\rangle}\) at the point \(\displaystyle{\left({0},\ {1},\ {1}\right)}\)
asked 2021-09-15
Find the principal unit normal vector to the curve at the specified value of the parameter
\(\displaystyle{r}{\left({t}\right)}={t}{i}+{\frac{{{6}}}{{{t}}}}{j},{t}={3}\)
asked 2021-05-07
Find a vector equation and parametric equations for the line segment that joins P to Q.
P(1, -1, 5), Q(5, 6, 1)
vector equation r(t) = ?
parametric equations (x(t), y(t), z(t)) = ?
asked 2021-06-12
Find the principal unit normal vector to the curve at the specified value of the parameter
\(r(t)=ti+\frac{6}{t}j , t=3\)
asked 2021-11-14
Identify the surface with the given vector equation.
\(\displaystyle{r}{\left({s},{t}\right)}={<}{s},{t},{t}^{{2}}-{s}^{{2}}{>}\)
asked 2021-09-22
Identify the surface with the given vector equation. r(s,t)=\(\displaystyle{\left({s},{t},{t}^{{2}}-{s}^{{2}}\right)}\)
eliptic cylinder
circular paraboloid
hyperbolic paraboloid
plane
circular cylinder
...