Question 1206873
If y^x = 5^y then dy/dx = ...
<pre>
{{{y^x}}}{{{""=""}}}{{{5^y}}}

Take natural logs of both sides:

{{{ln(y^x)}}}{{{""=""}}}{{{ln(5^y)}}}

{{{x*ln(y)}}}{{{""=""}}}{{{y*ln(5)}}}

{{{x((dy/dx)/y^"")+ln(y)*1=ln(5)*(dy/dx)}}}

Multiply through by y

{{{x(dy/dx)+y*ln(y)}}}{{{""=""}}}{{{y*ln(5)*(dy/dx)}}}

{{{x(dy/dx)-y*ln(5)*(dy/dx)}}}{{{""=""}}}{{{-y*ln(y)}}}

{{{(dy/dx)(x-y*ln(5)^"")}}}{{{""=""}}}{{{-y*ln(y)}}}

{{{dy/dx}}}{{{""=""}}}{{{(-y*ln(y))/(x-y*ln(5))}}}

Don't see that listed!!!

Edwin</pre>