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You can put this solution on YOUR website!
\n" ); document.write( "The solution by the other tutor can be simplified; but it is difficult to see how.
\r
\n" ); document.write( "\n" ); document.write( "The simpler form of the answer can be obtained more easily via a different path.
\n" ); document.write( "ln(ln(y))+ln(y) = ln(x)
\n" ); document.write( "Write the expression on the left as a single logarithm:
\n" ); document.write( "ln(y*ln(y)) = ln(x)
\n" ); document.write( "y*ln(y) = x
\n" ); document.write( "Now do the differentiation using the product rule:
\n" ); document.write( "y'(ln(y))+y(1/y)y' = 1
\n" ); document.write( "y'(ln(y))+y' = 1
\n" ); document.write( "y'(1+ln(y)) = 1
\n" ); document.write( "y' = 1/(1+ln(y))
\n" ); document.write( "The answer from the other tutor was this:
\n" ); document.write( "y' =(y*ln(y))/(x(1+ln(y)))
\n" ); document.write( "This is equivalent to
\n" ); document.write( "y' = 1/(1+ln(y))
\n" ); document.write( "because
\n" ); document.write( "y*ln(y) = x \n" ); document.write( "