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Calculus/Differentiate each equation implicityly

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Expert: Alon Mandes - 12/11/2008


Question
e^2xlnsquarerootofy- ln(e^2x)Xe^lny = xy

i am so confused on this problem

Answer
Hello Samantha,
When we are performing implicit derivatives , we have to keep in
mind two major rules :
1. if f(x,y)=xy then d/dx { f(x,y) } = d/dx {xy}.
2. d/dx {x} =1 & d/dy {y} = y'.
3. for example d/dx [xy] = x'y+y'x=y+xy'.
So, our implicit function is :
[e^2x][Ln(√y)]-[Ln(e^2x)][e^Ln(y)]=xy. Then we get :
d/dx { e^[2xLn(√y)]-[Ln(e^2x)][e^Ln(y)]=xy } = d/dx { xy }
[2Ln(√y)+(xy')/y]e^[2xLn(√y)]-2y-2xy'=y+xy'
All we need to do now is to express y' in terms of x & y.

Alon.  

Calculus

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Alon Mandes

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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 .

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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".

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

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M.A in Mathematics & Bs.c in Electronics.

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