Question

Use implicit differentiation to find the equation of the tangent line to the curve xy^3+2xy=9 at the point (31)

Use implicit differentiation to find the equation of the tangent line to the curve xy^3+2xy=9 at the point (31). The equation of this tangent line can be written in the form y=mx+b where m is
0 0
Add a comment Improve this question
Answer #1
x(3y^2dy) + y^3(dx) +2xdy + 2ydx = 0

dy (3xy^2+2x) = -dx (y^3+2y)

dy/dx = -(y^3+2y)/(3xy^2+2x)

I assume you mean the point (3,1)
x = 3
y = 1
so
m = dy/dx = -(1+2)/(9+6) = - 3/15 = -1/5
put in point
1 = m * 3 + b
1 = -3/5 + b
b = 8/5
y = -x/5 + 8/5
5y = 8-x
answered by: \margie
Add a comment
Know the answer?
Add Answer to:
Use implicit differentiation to find the equation of the tangent line to the curve xy^3+2xy=9 at the point (31)
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT