<PRE><B>Question 1119541</B>
&lt;br&gt;
The solution by the other tutor can be simplified; but it is difficult to see how.&lt;br&gt;

The simpler form of the answer can be obtained more easily via a different path.&lt;br&gt;
ln(ln(y))+ln(y) = ln(x)&lt;br&gt;
Write the expression on the left as a single logarithm:&lt;br&gt;
ln(y*ln(y)) = ln(x)&lt;br&gt;
y*ln(y) = x&lt;br&gt;
Now do the differentiation using the product rule:&lt;br&gt;
y&#39;(ln(y))+y(1/y)y&#39; = 1
y&#39;(ln(y))+y&#39; = 1
y&#39;(1+ln(y)) = 1
y&#39; = 1/(1+ln(y))&lt;br&gt;
The answer from the other tutor was this:&lt;br&gt;
y&#39; =(y*ln(y))/(x(1+ln(y)))&lt;br&gt;
This is equivalent to&lt;br&gt;
y&#39; = 1/(1+ln(y))&lt;br&gt;
because&lt;br&gt;
y*ln(y) = x</PRE>