Question

Use implicit differentiation to find an equation of the tangent line to the curve.

x^5y^5=32, tangent at (2,1)

Answer 1

know product rule, power rule, constant rule, and chain rule?

Answer 2

or if you want to make this really easy take the 5th root of both sides

Answer 3

if you know all the three rules mentioned by freckles then you can easily solve it :)

Answer 4

if you take the fifth root the equation would be : xy=2

Answer 5

slope : \(\Large \frac{dy}{dx}\)

Answer 6

Can one of you walk me through this ? Step by step ?

Answer 7

equation of tangent : \[\rm y-y_{1}=\frac{ dy }{ dx }(x-x_{1})\]

Answer 8

What about the derivative ?

Answer 9

you need to apply the rules (or at least some) to differentiate xy=2

Answer 10

xy is a product
so you would use the product rule to differentiate xy

Answer 11

2 is a constant
the constant rule says derivative of a constant is 0

Answer 12

(xy)'=0
can you apply the product rule to find (xy)'

Answer 13

you can go through this : Basic Derivatives http://openstudy.com/study#/updates/5550950fe4b061b8579d7c1d

Answer 14

What about the derivative ?

Answer 15

to differentiate is to find the derivative

Answer 16

(xy)' means find the derivative of the product of x and y

Answer 17

do you know how to find the derivative of the product of x and y

Answer 18

do you know the product rule?

Answer 19

actually if you don't know the product rule
@rvc has posted for you in that link

Answer 20

Yes I know the product rule ..

Answer 21

so apply the product rule to find (xy)'

Answer 22

yep :)
you may have a look at that

Answer 23

good then go for it
apply the product rule

Answer 24

Okay thank you !

Answer 25

All the best