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Calculus/implicit 2nd differentiation using calculus

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Expert: Alon Mandes - 1/2/2009


Question
Hello, I am very new to calculus and i would love to get some help. I have a question that i cannot determine. please help me and if you can please show work

d^2(x^6+5x^3+2x^2+8y)/dx^2
all letters are variables, there are no constants

Thank you for your time.

Answer
Hello Joseph,
In Implicit derivative we retreat y as a function of x, & we derive
y as well as we derive x. 2 major rules are involved here :
1. d/dx {f(x)} = f'(x)
2. d/dx {g(y)} = g'(y)*y'
In our case for example : d/dx{2x^2}=4*x & d/dx{8y}=8*y' .
Now let's solve the exercise :
d^2/dx^2 {x^6+5x^3+2x^2+8y} = d/dx {6x^5+15x^2+4x+8y') =
("Now we are deriving second time")
=30x^4+30x+4+8y''
Note that y'' is a function of x. That's why these function are called implicit.

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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