A community for students.
Here's the question you clicked on:
 0 viewing

This Question is Open

RoyTheRoyalBoy
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ bxa ^{x1}+x ^{2}a ^{x1}a ^{x} }{ (b+x)^{2} }\]

creeksider
 one year ago
Best ResponseYou've already chosen the best response.1In this problem, a and b are constants, so the only variable is x. You have a quotient, so we have to apply the quotient rule:\[\frac{ d }{ dx }\frac{ u }{ v }=\frac{ vu'uv' }{ v^2 }\]In this problem,\[u=ax, u'=a, v=b+x, v'=1\]Therefore we get \[\frac{ d }{ dx }\frac{ ax }{ b+x }=\frac{ (b+x)aax }{ (b+x)^2 }\]The numerator expands to ba+xaax which is equal to ba, so the answer is \[\frac{ ba }{ (b+x)^2 }\]The interesting point about this exercise is that the variable x disappears from the numerator, so that we have only the constant ba. That's not surprising when you consider that the original formula can be changed as follows, where the first step involves adding and subtracting the same number, so we're just adding zero:\[\frac{ ax }{ b+x }=\frac{ ax+abab }{ b+x }=\frac{ a(b+x)ab }{ b+x }=a\frac{ ab }{ b+x }\]Because a is a constant and the derivative of a constant is zero, your answer is the same as what you would get if you simply find the derivative of ab/(b+x).
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.