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?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

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?

OCW Scholar - Single Variable Calculus
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

If\[V =\frac{ 1 }{ 3 }\pi(\frac{ 2 }{ 5 }h)^{2}h\]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?
Is 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.
The second equation is with h cubed. I'm glad you understand.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

but how do you actually get the derivative that was obtained by the professor?
@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\[\frac{ dV }{ dt }=(3)(\frac{ 4\pi }{ 75 })(h ^{2})(\frac{ dh }{ dt })\] \[\frac{ dV }{ dt }=\frac{ 4\pi }{ 25 }h ^{2}\frac{ dh }{ dt }\]
When we differentiate the constants just sort of tag along.|dw:1351220408198:dw|

Not the answer you are looking for?

Search for more explanations.

Ask your own question