lili.gallegos
  • lili.gallegos
Use implicit differentiation to find an equation of the tangent line to the curve. x^5y^5=32, tangent at (2,1)
Mathematics
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katieb
  • katieb
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freckles
  • freckles
know product rule, power rule, constant rule, and chain rule?
freckles
  • freckles
or if you want to make this really easy take the 5th root of both sides
rvc
  • rvc
if you know all the three rules mentioned by freckles then you can easily solve it :)

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rvc
  • rvc
if you take the fifth root the equation would be : xy=2
rvc
  • rvc
slope : \(\Large \frac{dy}{dx}\)
lili.gallegos
  • lili.gallegos
Can one of you walk me through this ? Step by step ?
rvc
  • rvc
equation of tangent : \[\rm y-y_{1}=\frac{ dy }{ dx }(x-x_{1})\]
lili.gallegos
  • lili.gallegos
What about the derivative ?
freckles
  • freckles
you need to apply the rules (or at least some) to differentiate xy=2
freckles
  • freckles
xy is a product so you would use the product rule to differentiate xy
freckles
  • freckles
2 is a constant the constant rule says derivative of a constant is 0
freckles
  • freckles
(xy)'=0 can you apply the product rule to find (xy)'
rvc
  • rvc
you can go through this : Basic Derivatives http://openstudy.com/study#/updates/5550950fe4b061b8579d7c1d
lili.gallegos
  • lili.gallegos
What about the derivative ?
freckles
  • freckles
to differentiate is to find the derivative
freckles
  • freckles
(xy)' means find the derivative of the product of x and y
freckles
  • freckles
do you know how to find the derivative of the product of x and y
freckles
  • freckles
do you know the product rule?
freckles
  • freckles
actually if you don't know the product rule @rvc has posted for you in that link
lili.gallegos
  • lili.gallegos
Yes I know the product rule ..
freckles
  • freckles
so apply the product rule to find (xy)'
rvc
  • rvc
yep :) you may have a look at that
rvc
  • rvc
good then go for it apply the product rule
lili.gallegos
  • lili.gallegos
Okay thank you !
rvc
  • rvc
All the best

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