x^y=e^x-y prove dy/dx=lnx/(1+lnx)^2

x^y=e^x-y prove dy/dx=lnx/(1+lnx)^2
in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

8 Answers

Applying the operator ln^,
by Level 12 User (101k points)
On both sides of the given equality we have :
by Level 12 User (101k points)
Y lnx=x-y
by Level 12 User (101k points)
→ y(1+lnx)=x
by Level 12 User (101k points)
→ y= x/1+lnx
by Level 12 User (101k points)
Therefore, dy/dx_= y'
by Level 12 User (101k points)
= x'•(1+lnx)-x•(0+1/x)/(1+lnx)^2
by Level 12 User (101k points)
=1+lnx-1/(1+lnx)^2
by Level 12 User (101k points)

Related questions

9 answers
x^y=e^x-y , prove that dy/dx=lnx/(1+lnx)^2
asked Jan 25, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 1.8k views
1 answer
solve dy/dx-y=e^x/x given that y(e)=0
asked Mar 11, 2016 in Calculus Answers by anonymous | 883 views
11 answers
If y=e^(ax)cos^3 x sin^2 x find dy/dx
asked May 31, 2013 in Calculus Answers by anonymous | 2.6k views
0 answers
(e^x+y+ye^y)dx+(x^y-1)dy=0
asked Mar 22, 2014 in Other Math Topics by Keys Lee | 668 views
13 answers
if Y=e^ax•COS^3 X•SIN^2 X find dy/dx
asked Jan 24, 2014 in Algebra 2 Answers by Jennifer A. Cascaño Level 12 User (101k points) | 3.1k views
1 answer
show that (1-x^2)dy/dx+y=0
asked Jun 22, 2017 in Calculus Answers by Poulami | 702 views
2 answers
dy/dx=cos(x+y), y(0)=PI/4
asked Jan 29, 2016 in Calculus Answers by John | 6.9k views
1 answer
solve the verhulst DE dy/dx=0.5y(1-y/5)
asked Oct 8, 2014 in Calculus Answers by miah | 882 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular questions within the last 3000 days

  1. 50+50-25X0+2+2= (19)
  2. it takes 10 road workers 5 days to complete a road repair when working 2 hours a day.Working at the same pace,how many days will it take 2 people working 5 hours a day to finish it? (3)
  3. Solve 15 -1(12÷4+1)? (4)
  4. 8:4(5+2) (3)
  5. How can i represent 1/3; 3/3; 7/3; 10/3 and 15/3 on a number line? (1)

Most popular tags

87,516 questions
100,279 answers
2,420 comments
731,653 users