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Calculus/Solve this derivative problem

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Expert: Alon Mandes - 12/12/2010


Question
How to find the partial derivatives?
If f(x, y) = 6x^2 + 2e^xy, find the following.

(a) ∂^2f /∂x^2


(b) ∂^2f /∂y ∂x


(c) ∂^2f /∂x ∂y

(d) ∂^2f /∂y^2


Answer
The key is to treat each variable a seperate one .
Now, if you meant that f(x,y) is
f(x,y)=6x²+2e^(xy)
then
∂f/∂x = 12x+2ye^(xy) ("we treat y as a parameter")
∂f/∂y = 0+2xe^(xy)  ("we treat x as a parameter")
∂²f/∂x² = ∂/∂x{∂f/∂x} = 12+2y²e^(xy) ("2nd derivative")
∂²f/∂y² = ∂/∂y{∂f/∂y} = 2x²e^(xy)  ("2nd derivative")
∂²f/∂x∂y = ∂/∂y{∂f/∂x} = ∂/∂y {12x+2ye^(xy)}=2e^(xy)+2yxe^(xy).
∂²f/∂y∂x = ∂/∂x{∂f/∂y} = ∂/∂x {0+2xe^(xy)}=2e^(xy)+2xye^(xy).

Alon.  

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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 .

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".

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

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

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