Calculus/derivative

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Expert: Alon Mandes - 12/20/2009


Question
I've been staring at this problem for a very long time. I know that I have to use chain and product rules, but I just can't get it:

What is the derivative of : ((4x)^(1/2))(6x+2)^4
-- 4x to the 1/2 multiplied by 6x+2 to the 4th

Answer
f(x)=[(4x)^(1/2)]*[(6x+2)^4]=[2x^(1/2)][(6x+2)^4]
f'(x)=[(2x)^(1/2)]'*[(6x+2)^4]+[(2x)^(1/2)]*[(6x+2)^4]'
f'(x)=(2/2)[x^(-1/2)]*[(6x+2)^4]+[2x^(1/2)]*4*6*[(6x+2)^3]
f'(x)=[x^(-1/2)]*[(6x+2)^4]+48[x^(1/2)][(6x+2)^3]
f'(x)= { (6x+2)^4 + 48x[(6x+2)^3] } / { x^(1/2) }
f'(x)= (6x+2)^3 * [ 6x+2+48x ]  /  x^(1/2)
f'(x)= (6x+2)^3 * [ 54x+2 ]  /  x^(1/2)

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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