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.

13,459 questions

17,854 answers

1,446 comments

802,442 users

derivative of function!!!!!!!!!!!!!!!

0 votes

f(x)=xlnx-x

asked Jun 29, 2013 in CALCULUS by rockstar Apprentice

1 Answer

0 votes

Given that f(x) = xlogx - x = y

Differentiating on both sides we get,

                   dy/dx = d/dx(xlogx - x)

                             = d/dx(xlogx) - dx/dx            

                             = xd/dx(logx) + logxd/dx(x) - 1    [Product rule d/dx(uv) = uv' + vu' and d/dx(x) = 1]

                             = x(1/x) + logx(1) - 1                  [Since d/dx(logx) = 1/x and d/dx(x) = 1]

                             = 1 + logx - 1

                             = logx

Therefore dy/dx = logx

 

answered Jun 29, 2013 by joly Scholar

Related questions

asked Feb 16, 2015 in CALCULUS by anonymous
asked Nov 6, 2014 in CALCULUS by anonymous
asked Sep 24, 2014 in CALCULUS by anonymous
asked Oct 24, 2014 in CALCULUS by anonymous
asked Oct 20, 2014 in CALCULUS by anonymous
...