Ask your own question, for FREE!
Mathematics
OpenStudy (anonymous):

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

OpenStudy (anonymous):

Basically, I answered the question with 9x^2+2, but I was wrong and I'm trying to figure out why. :(

OpenStudy (shadowfiend):

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.

OpenStudy (shadowfiend):

Well, chain rule + product rule.

OpenStudy (anonymous):

So would t/5t+1 be equal to 2/(5t+1)^2?

OpenStudy (shadowfiend):

Heh, I totally messed the thing up there up. $\frac{t}{9t + 2} = t(9t + 2)^{-1}$

OpenStudy (shadowfiend):

No, it wouldn't derive to that. It would derive to 1/(5t + 1)^2.

OpenStudy (shadowfiend):

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}

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
NoodlesAndRiceYT: i think i found a glitch, sometimes when i log into questioncove, this happens an
23 minutes ago 25 Replies 3 Medals
14xavierrobinson: what is discrimination
1 hour ago 1 Reply 0 Medals
quasia: Who were the members of each alliance in World War I?
2 hours ago 5 Replies 1 Medal
Vocaloid: AP Calc BC Study Guide/Tutorial
2 hours ago 1 Reply 7 Medals
NoProbBob: Help Yo SS below
2 hours ago 15 Replies 1 Medal
yallbabynene08: help
1 hour ago 20 Replies 2 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!