Why is ds/dt of s=t/9t+2 = 2/(9t+2)^2 and not the derivative 9x^2+2?

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.

Why is ds/dt of s=t/9t+2 = 2/(9t+2)^2 and not the derivative 9x^2+2?

Mathematics
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

Basically, I answered the question with 9x^2+2, but I was wrong and I'm trying to figure out why. :(
Well, when you have an equation divided by another equation, you have to apply the quotient rule or the chain rule. I prefer the chain rule, personally. So: \[\frac{t}{9t + 2} = t^{-1}(9t + 2)\] If you apply the chain rule to that, the answer might make a bit more sense.
Well, chain rule + product rule.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

So would t/5t+1 be equal to 2/(5t+1)^2?
Heh, I totally messed the thing up there up. \[\frac{t}{9t + 2} = t(9t + 2)^{-1}\]
No, it wouldn't derive to that. It would derive to 1/(5t + 1)^2.
You do this by saying: \[\frac{ds}{dt}t(5t+1)^{-1}\] \[\begin{align} (5t + 1)^{-1} + t(-1)(5t + 1)^{-2}(5)\\ \frac{1}{5t + 1} - \frac{5t}{(5t + 1)^2}\\ \frac{5t + 1}{(5t+1)^2} - \frac{5t}{(5t + 1)^2}\\ \frac{5t + 1 - 5t}{(5t + 1)^2}\\ \frac{1}{(5t + 1)^2} \end{align}\]

Not the answer you are looking for?

Search for more explanations.

Ask your own question