## lili.gallegos one year ago Use implicit differentiation to find an equation of the tangent line to the curve. x^5y^5=32, tangent at (2,1)

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1. freckles

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

2. freckles

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

3. rvc

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

4. rvc

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

5. rvc

slope : $$\Large \frac{dy}{dx}$$

6. lili.gallegos

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

7. rvc

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

8. lili.gallegos

9. freckles

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

10. freckles

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

11. freckles

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

12. freckles

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

13. rvc

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

14. lili.gallegos

15. freckles

to differentiate is to find the derivative

16. freckles

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

17. freckles

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

18. freckles

do you know the product rule?

19. freckles

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

20. lili.gallegos

Yes I know the product rule ..

21. freckles

so apply the product rule to find (xy)'

22. rvc

yep :) you may have a look at that

23. rvc

good then go for it apply the product rule

24. lili.gallegos

Okay thank you !

25. rvc

All the best