You are here:

Calculus/Implicit Differentiation Help!

Advertisement

Expert: Alon Mandes - 3/21/2009


Question
1. Use implicit differentiation to find the equation of the tangent line to the curve xy^3+xy=16 at the point (8,1). The equation of this tangent line can be written in the form y=mx=b where m is: ______ and where b is: ________

2. find the slope of the tangent line to the curve
-3x^2-4xy-2y^3=-12 at the point (-2,2) .

3. Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2=25(x^2-y^2) at the point (3,-1).

4. If 3x^2+3x+xy=4 and y(4)=-14, find y'(4) by implicit differentiation.

5. If (x^2)/(49) + (y^2)/(16)+1 and y(2)=3.83326, find y'(2) by implicit differentiation.  

Answer
I will solve (2) & (5) , the others I will leave it for you as an
exercise :

-3x^2-4xy-2y^3=-12 Let's derive both sides with respect to y(x) :
-6x-4y-4xy'-6y^2=0
-4xy'=6x+4y+6y^2
y'(x,y)=-(6x+4y+6y^2)/(4x)
y'(-2,2)=-(-12+8+24)/(-8)
y'(-2,2)=20/8=5/2=2.5
------------------------

(x^2)/(49)+(y^2)/(16)=1 Let's derive both sides :
(2/49)x+yy'/8=1
Let's substitute x=2 & y(2)=3.833 :
(2/49)*2+(3.833/8)*y'(2)=1

0.081 + 0.479*y'(2)=1
0.479*y'(2)=0.919
y'(2)=1.91

Alon.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.