Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Open

.Sam.Best ResponseYou've already chosen the best response.0
Looks like implicit differentiation, do you know how to approach this problem?
 one year ago

YLynnBest ResponseYou've already chosen the best response.0
a bit. yes, it is implicit differentiation
 one year ago

.Sam.Best ResponseYou've already chosen the best response.0
Here, most of the work involve chain rule only
 one year ago

YLynnBest ResponseYou've already chosen the best response.0
differentiate each term d/dx ( ln x ) + d/dx (ln (y)
 one year ago

YLynnBest ResponseYou've already chosen the best response.0
how can you tell by looking at the equation
 one year ago

.Sam.Best ResponseYou've already chosen the best response.0
Differentiate (x+2)^2 you'll get 2(x+2) Differentiate 6(2y+3)^2 you'll get 12(2y+3)(2)(dy/dx) The 2 comes from chain rule, and dy/dx is differentiating with respect to x . Differentiate 3 is 0 Then you'll get \[2(x+2)12(2y+3)(2)\frac{dy}{dx}=0\] \[2(x+2)24(2y+3)\frac{dy}{dx}=0\] \[\frac{dy}{dx}=\frac{x+2}{24 y+36}\]
 one year ago

.Sam.Best ResponseYou've already chosen the best response.0
Because there's 2 terms together with a power, you'll have to use chain rule
 one year ago

.Sam.Best ResponseYou've already chosen the best response.0
Examples, 1) Differentiate 3(x+6)^2 dy/dx=6(x+6) 2) Differentiate 3(4x+2)^2 dy/dx=6(4x+2)(4) dy/dx=24(4x+2)
 one year ago

YLynnBest ResponseYou've already chosen the best response.0
ok. thanks for the examples. I understand those. For the question, the book gives an answer of: y'= 1/4 ?
 one year ago

AzteckBest ResponseYou've already chosen the best response.0
\[\huge D_{x}[(x+2)^26(2y+3)^2]=0\] \[\huge 2(x+2)24(\frac{dy}{dx})(2x+3)=0\] Divide both sides by 2. \[\huge (x+2)12(\frac{dy}{dx})(2x+3)=0\] Make dy/dx the subject. \[\huge \frac{dy}{dx}12(2x+3)=(x+2)\] \[\huge \frac{dy}{dx}=\frac{x+2}{12(2x+3)}\] At (1, 1) \[\huge \frac{dy}{dx}=\frac{1+2}{12[2(1)+3]}\] \[\huge \frac{dy}{dx}=\frac{3}{12(2+3)}\] \[\huge \frac{dy}{dx}=\frac{3}{12}\] \[\huge =\frac{1}{4}\]
 one year ago

AzteckBest ResponseYou've already chosen the best response.0
Use chain rule when differentiating in this situation.
 one year ago
See more questions >>>
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.