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
having a little bit of trouble remembering how to do the differential.
 one year ago
 one year ago
richyw Group Title
having a little bit of trouble remembering how to do the differential.
 one year ago
 one year ago

This Question is Closed

richyw Group TitleBest ResponseYou've already chosen the best response.0
so I have \(k(x,y,z)=e^{x^2+y^2+z^2}\) where \(x=\sqrt{t+1},\;y=\sqrt{t^2+1},\:z=\sqrt{t^3+1}\) . Now i need to find \(\frac{dk}{dt}\).
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
to do this do I just say\[\frac{dk}{dt}=\frac{dk}{dx}\frac{dx}{dt}+\frac{dk}{dy}\frac{dy}{dt}+\frac{dk}{dz}\frac{dz}{dt}\]
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
I am getting an answer of \[\frac{dk}{dt}=2e^{t^3+t^2+t+3}\left(3t^2+2t+1\right)\] is this correct, and does anyone know how to check this on wolfram, or opensource math software?
 one year ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
The formula for the total differential is correct, as long as the dk/dx,etc terms are partial derivatives.
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
yeah sorry I didn't want to type "partial" \(\partial\) in the latex that many times :)
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
thanks a lot. can anyone confirm this is the correct answer?
 one year ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
this one is super tedious...give me a minute I'll do it with pen and paper...
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
alright thanks a lot. I really appreciate it.
 one year ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
I get:\[e^{t^3+t^2+t+3}(3t^2+2t+1)\]
 one year ago

eseidl Group TitleBest ResponseYou've already chosen the best response.1
Your factor of two should cancel when you differentiate the square root term (which gives you a 2 in the denominator)...
 one year ago

richyw Group TitleBest ResponseYou've already chosen the best response.0
thanks a lot! I see I made a basic calculus mistake but am glad I remember this stuff!
 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.