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

x^y=e^x-y , prove that dy/dx= lnx/(1+lnx)^2
in Calculus Answers by Level 12 User (101k points)

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.

9 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)
Ylnx=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)
= lnx/(1+lnx)^2
by Level 12 User (101k points)

Related questions

8 answers
x^y=e^x-y prove dy/dx=lnx/(1+lnx)^2
asked Jan 19, 2013 in Calculus Answers by anonymous | 1.7k 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 | 701 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
45 answers
solve: (x+y•sin^2(y/x)) dx=x^2 SIN(y/x) dy
asked Feb 1, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 5.3k views
10 answers
how can you prove that (xy+1)dx+x•(x+4y2dy=0
asked Jan 29, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 1.7k views
16 answers
solve: (2x+3y-1) dx+(2x+3y-5) dy=0
asked Feb 1, 2014 in Calculus Answers by Jennifer A. Cascaño Level 12 User (101k points) | 3.1k 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
731,646 users