A community for students.
Here's the question you clicked on:
 0 viewing
sjmoneys96
 3 years ago
In the third video on related rates the Professor differentiates 1/3pi(2h/5)^2h and gets pi/3(2/5)^2(3h^2)(dh/dt). How did he get this? I know you're trying to find rate of change of h with respect to t. So I get the dh/dt at the end, I guess I am just getting confused on some usage of the chain rule. Can anyone help?
sjmoneys96
 3 years ago
In the third video on related rates the Professor differentiates 1/3pi(2h/5)^2h and gets pi/3(2/5)^2(3h^2)(dh/dt). How did he get this? I know you're trying to find rate of change of h with respect to t. So I get the dh/dt at the end, I guess I am just getting confused on some usage of the chain rule. Can anyone help?

This Question is Open

calculusfunctions
 3 years ago
Best ResponseYou've already chosen the best response.1If\[V =\frac{ 1 }{ 3 }\pi(\frac{ 2 }{ 5 }h)^{2}h\]If we simplify this, we get\[V =\frac{ 4\pi }{ 75 }h ^{3}\]I haven't differentiated yet because first I wanted to know if you understand what I have done here, first. Do you understand?

sjmoneys96
 3 years ago
Best ResponseYou've already chosen the best response.0Is that an h^3 at the end of the equation or an h^2? If it is an h^3 then yes I do understand. I thought it was an h^2, but then when I went to type a reply i realized that the equation editor on this site makes the h^2 and h^3's look exactly the same.

calculusfunctions
 3 years ago
Best ResponseYou've already chosen the best response.1The second equation is with h cubed. I'm glad you understand.

sjmoneys96
 3 years ago
Best ResponseYou've already chosen the best response.0but how do you actually get the derivative that was obtained by the professor?

calculusfunctions
 3 years ago
Best ResponseYou've already chosen the best response.1@sjmoneys96 In related rate problems we differentiate all unknown quantifiable variables with respect to time. Thus if\[V =\frac{ 4\pi }{ 75 }h ^{3}\]then\[\frac{ dV }{ dt }=(3)(\frac{ 4\pi }{ 75 })(h ^{2})(\frac{ dh }{ dt })\] \[\frac{ dV }{ dt }=\frac{ 4\pi }{ 25 }h ^{2}\frac{ dh }{ dt }\]

Stacey
 3 years ago
Best ResponseYou've already chosen the best response.0When we differentiate the constants just sort of tag along.dw:1351220408198:dw
Ask your own question
Sign UpFind more explanations on OpenStudy
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.