Calculus/Intro

Advertisement

Expert: Alon Mandes - 7/27/2009


Question
Please I really need help with this:
Differentiation:
1/3x^6(x^2-3)

5/square root 4+x

1/2square root 3x-1

Answer
If you mean f(x)=1/[3x^6*(x²-3)] then
f'(x)=1/{ [3x^6*(x²-3)]² } * {3x^6*(x²-3)}'
=1/{ [3x^6*(x²-3)]² } * { [3x^6]'*(x²-3)+[3x^6]*(x²-3)' }
=1/{ [3x^6*(x²-3)]² } * { [18x^5]*(x²-3)+[3x^6]*(2x) }
=1/{ [3x^6*(x²-3)]² } * { 18x^7-54x^5+6x^7 }
=1/{ [3x^6*(x²-3)]² } * { 24x^7-54x^5 } .

If you mean f(x)=[1/3x^6]*[x²-3] then
f'(x)=[1/3x^6]'*[x²-3]+[1/3x^6]*[x²-3]'
=[1/3x^12]*(6x^5)*[x²-3]+[1/3x^6]*[2x]
=[2/x^7]*[x²-3]+[2/3x^7]
=[2/x^7]*[x²-3+⅓].

[5/√(4+x) ]'=5*[√(4+x)]'/(4+x)=5/[2(4+x)^(3/2)].
[1/2√(3x+1)]'=½(3x+1)^(-½)=-¾(3x+1)^(-3/2) .

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.