SOLUTION: If y^x = 5^y then dy/dx = .... [(1 +lnx)y , (1- lnx)y , (1+1/x)y , (1- 1/x)y]

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: If y^x = 5^y then dy/dx = .... [(1 +lnx)y , (1- lnx)y , (1+1/x)y , (1- 1/x)y]      Log On


   

Question 1206873: If y^x = 5^y then dy/dx = ....
[(1 +lnx)y , (1- lnx)y ,
(1+1/x)y , (1- 1/x)y]
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
If y^x = 5^y then dy/dx = ...
y%5Ex%22%22=%22%225%5Ey

Take natural logs of both sides:

ln%28y%5Ex%29%22%22=%22%22ln%285%5Ey%29

x%2Aln%28y%29%22%22=%22%22y%2Aln%285%29

x%28%28dy%2Fdx%29%2Fy%5E%22%22%29%2Bln%28y%29%2A1=ln%285%29%2A%28dy%2Fdx%29

Multiply through by y

x%28dy%2Fdx%29%2By%2Aln%28y%29%22%22=%22%22y%2Aln%285%29%2A%28dy%2Fdx%29

x%28dy%2Fdx%29-y%2Aln%285%29%2A%28dy%2Fdx%29%22%22=%22%22-y%2Aln%28y%29

%28dy%2Fdx%29%28x-y%2Aln%285%29%5E%22%22%29%22%22=%22%22-y%2Aln%28y%29

dy%2Fdx%22%22=%22%22%28-y%2Aln%28y%29%29%2F%28x-y%2Aln%285%29%29

Don't see that listed!!!

Edwin

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

This problem is posed incorrectly, since NO ONE of listed options is a correct answer.