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YLynn
 2 years ago
how do I find dy/dx at:
(x+2)^26(2y+3)^2=3, (1, 1)
YLynn
 2 years ago
how do I find dy/dx at: (x+2)^26(2y+3)^2=3, (1, 1)

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

YLynn
 2 years ago
Best ResponseYou've already chosen the best response.0a bit. yes, it is implicit differentiation

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

YLynn
 2 years ago
Best ResponseYou've already chosen the best response.0differentiate each term d/dx ( ln x ) + d/dx (ln (y)

YLynn
 2 years ago
Best ResponseYou've already chosen the best response.0how can you tell by looking at the equation

.Sam.
 2 years ago
Best ResponseYou've already chosen the best response.0Differentiate (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 \[2(x+2)12(2y+3)(2)\frac{dy}{dx}=0\] \[2(x+2)24(2y+3)\frac{dy}{dx}=0\] \[\frac{dy}{dx}=\frac{x+2}{24 y+36}\]

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

.Sam.
 2 years ago
Best ResponseYou've already chosen the best response.0Examples, 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)

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

Azteck
 2 years ago
Best 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) \[\huge \frac{dy}{dx}=\frac{1+2}{12[2(1)+3]}\] \[\huge \frac{dy}{dx}=\frac{3}{12(2+3)}\] \[\huge \frac{dy}{dx}=\frac{3}{12}\] \[\huge =\frac{1}{4}\]

Azteck
 2 years ago
Best ResponseYou've already chosen the best response.0Use chain rule when differentiating in this situation.
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