Loading [MathJax]/extensions/mml2jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

Search

  • Filter Results
  • Location
  • Classification
    • Article type
    • Stage
    • Author
    • Cover Page
    • License
    • Show Page TOC
    • Transcluded
    • PrintOptions
    • OER program or Publisher
    • Autonumber Section Headings
    • License Version
    • Print CSS
    • Screen CSS
    • Number of Print Columns
  • Include attachments
Searching in
About 3 results
  • 13.2b: The Calculus of Vector-Valued Functions II
    https://math.libretexts.org/Courses/Montana_State_University/M273%3A_Multivariable_Calculus/13%3A_Vector-valued_Functions/13.2b%3A_The_Calculus_of_Vector-Valued_Functions_II
    We now find \(\vecs u\,'(t)\) using part 3 of Theorem 92: \[\begin{align*}\vecs u\,'(t) &= f^\prime (t)\vecs u(t) + f(t)\vecs u\,'(t) \\&= -\frac{2t(2t^2-1)}{2\big(\sqrt{t^2+(t^2-1)^2}\,\big)^3}\langl...We now find \(\vecs u\,'(t)\) using part 3 of Theorem 92: \[\begin{align*}\vecs u\,'(t) &= f^\prime (t)\vecs u(t) + f(t)\vecs u\,'(t) \\&= -\frac{2t(2t^2-1)}{2\big(\sqrt{t^2+(t^2-1)^2}\,\big)^3}\langle t,t^2-1\rangle + \frac{1}{\sqrt{t^2+(t^2-1)^2}}\langle 1,2t\rangle.\end{align*}\]
  • 13.2B: The Calculus of Vector-Valued Functions II
    https://math.libretexts.org/Courses/Misericordia_University/MTH_226%3A_Calculus_III/Chapter_13%3A_Vector-valued_Functions/13.2B%3A_The_Calculus_of_Vector-Valued_Functions_II
    We now find \(\vecs u\,'(t)\) using part 3 of Theorem 92: \[\begin{align*}\vecs u\,'(t) &= f^\prime (t)\vecs u(t) + f(t)\vecs u\,'(t) \\&= -\frac{2t(2t^2-1)}{2\big(\sqrt{t^2+(t^2-1)^2}\,\big)^3}\langl...We now find \(\vecs u\,'(t)\) using part 3 of Theorem 92: \[\begin{align*}\vecs u\,'(t) &= f^\prime (t)\vecs u(t) + f(t)\vecs u\,'(t) \\&= -\frac{2t(2t^2-1)}{2\big(\sqrt{t^2+(t^2-1)^2}\,\big)^3}\langle t,t^2-1\rangle + \frac{1}{\sqrt{t^2+(t^2-1)^2}}\langle 1,2t\rangle.\end{align*}\]
  • The Calculus of Vector-Valued Functions II
    https://math.libretexts.org/Courses/Georgia_State_University_-_Perimeter_College/MATH_2215%3A_Calculus_III/13%3A_Vector-valued_Functions/The_Calculus_of_Vector-Valued_Functions_II
    We now find \(\vecs u\,'(t)\) using part 3 of Theorem 92: \[\begin{align*}\vecs u\,'(t) &= f^\prime (t)\vecs u(t) + f(t)\vecs u\,'(t) \\&= -\frac{2t(2t^2-1)}{2\big(\sqrt{t^2+(t^2-1)^2}\,\big)^3}\langl...We now find \(\vecs u\,'(t)\) using part 3 of Theorem 92: \[\begin{align*}\vecs u\,'(t) &= f^\prime (t)\vecs u(t) + f(t)\vecs u\,'(t) \\&= -\frac{2t(2t^2-1)}{2\big(\sqrt{t^2+(t^2-1)^2}\,\big)^3}\langle t,t^2-1\rangle + \frac{1}{\sqrt{t^2+(t^2-1)^2}}\langle 1,2t\rangle.\end{align*}\]

Support Center

How can we help?