Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
richyw
Group Title
Help! Vectorvalued functions.
define \(f:\mathbb{R}^2\rightarrow\mathbb{R}^3\) by \(f(u,v)=(u^25v,ve^{2u},2u\log(1+v^2))\). Suppose \(g:\mathbb{R}^2\rightarrow \mathbb{R}^2\) is of class \(C^1\), \(g(1,2)=(0,0)\) and \[Dg(1,2)=\left[\begin{matrix} 1 & 2 \\ 3 & 5\end{matrix}\right]\]Compute \(D(f\circ g)(1,2)\)
 one year ago
 one year ago
richyw Group Title
Help! Vectorvalued functions. define \(f:\mathbb{R}^2\rightarrow\mathbb{R}^3\) by \(f(u,v)=(u^25v,ve^{2u},2u\log(1+v^2))\). Suppose \(g:\mathbb{R}^2\rightarrow \mathbb{R}^2\) is of class \(C^1\), \(g(1,2)=(0,0)\) and \[Dg(1,2)=\left[\begin{matrix} 1 & 2 \\ 3 & 5\end{matrix}\right]\]Compute \(D(f\circ g)(1,2)\)
 one year ago
 one year ago

This Question is Closed

richyw Group TitleBest ResponseYou've already chosen the best response.0
so I know that\[Df=\left[\begin{matrix} 2u & 5 \\ 2ve^{2u} & e^{2u} \\ 2 & \frac{2v}{1+v^2}\end{matrix}\right]\]
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
why wouldn't this just be \[Df(1,2)\cdot Dg(1,2)\]
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.0
If you were looking for \(D(f+g)(1,2)\) you could simplify as \(Df(1,2)+Dg(1,2)\), but differentiation is only linear with respect to addition. If you multiplied your functions together, you need to use the chain rule.
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.