Ask your own question, for FREE!
Mathematics 7 Online
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
XShawtyX: Art, Short Writing Assignment: Imagining Landscapes
7 hours ago 2 Replies 0 Medals
XShawtyX: Chemistry, Help ud83dude4fud83cudffe
7 hours ago 13 Replies 1 Medal
kaelynw: tried a lil smt, the arm is off but i like the other stuff
18 hours ago 27 Replies 3 Medals
kaelynw: art igg
17 hours ago 14 Replies 2 Medals
XShawtyX: Art
3 days ago 6 Replies 0 Medals
Nina001: teach me how to draw or just tell me the basics
3 days ago 2 Replies 1 Medal
XShawtyX: We doing another drawing gimme ideas to add to this
3 days ago 9 Replies 1 Medal
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!