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

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

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

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

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

.Sam. Group TitleBest 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. Group TitleBest 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. Group TitleBest 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

YLynn Group TitleBest 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

Azteck Group TitleBest 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

Azteck Group TitleBest ResponseYou've already chosen the best response.0
Use chain rule when differentiating in this situation.
 one year ago
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