Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
youngbuck2123
Group Title
How would you use implicit differentiation to find an equation of the tangent line to the curve
x^2+ 2xyy^2+x=2 at the point (1,2)
 2 years ago
 2 years ago
youngbuck2123 Group Title
How would you use implicit differentiation to find an equation of the tangent line to the curve x^2+ 2xyy^2+x=2 at the point (1,2)
 2 years ago
 2 years ago

This Question is Closed

myininaya Group TitleBest ResponseYou've already chosen the best response.1
First step: Take derivative with respect to x on both sides of the equation.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[ (x^2+2xyy^2+x)'=(2)'\]  \[(x^2+2xyy^2+x)'=(x^2)'+(2xy)'(y^2)'+(x)'=....\] \[\text{Here you will need power rule for } (x^2)'\] \[\text{You will need constant multiple rule along with product rule for } (2xy)'\] \[\text{You will need chain rule for } (y^2)'\] \[\text{You will need to know that }(x)'=1 \text{ for the } (x)' \text{part}\]  \[(2)'=....\] You should know the derivative of a constant. :) 
 2 years ago

youngbuck2123 Group TitleBest ResponseYou've already chosen the best response.0
i understand the steps i just cannot put 2 and 2 together and get the correct final answer. i got 1/3 as the slope, is the correct?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Hmm...Not getting 1/3.... Show me your work so I can see where you messed up. You can do it one line at a time if you want.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\text{What did you get when you did } (2xy)' \text{ and } (y^2)' ?\]
 2 years ago

youngbuck2123 Group TitleBest ResponseYou've already chosen the best response.0
(2xy)' = dy/dx 2y +2x dy/dx and (y^2)' = 2y
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Looks incorrect for both
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[(2xy)' =2(xy)' \text{ By constant multiple rule}\] \[2(xy)'=2[xy]'=2[(x)'y+x(y)'] \text{ By product rule }\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[(y^n)'=n y ^{n1} y' \text{ By chain rule } \]
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.