Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

771,153 users

What is the derivative of

0 votes

(x/3^x)?

asked Jul 3, 2013 in CALCULUS by dkinz Apprentice

1 Answer

0 votes

d/dx(x / 3^x) = ( 3^x(d/dx(x)) - x d/dx(3^x) ) / (3^x)^2

This is in the form d/dx (u/v) which is equal to (vdu/dx - udv/dx) / v^2

                   = ( 3^x(1) - x (3^xlog3) ) / (3^x)^2

                   = 3^x [1 - x log3]  / (3^x)^2                       [Since d/dx(x) = 1, d/dx(a^x) = a^xloga]

                   = [1 - x log3]  / (3^x)

                   = (1 -  log3^x)  / (3^x)                                [Since nloga = loga^n]

Therefore d/dx(x / 3^x) = (1 -  log3^x)  / (3^x)    

answered Jul 3, 2013 by joly Scholar

Related questions

asked Nov 6, 2014 in CALCULUS by anonymous
asked Oct 20, 2014 in CALCULUS by anonymous
asked Sep 24, 2014 in CALCULUS by anonymous
...