Question 650758
<pre>
3x² - y² = 12

6x{{{(dx)/(dx)}}} - 2y{{{(dy)/(dx)}}} = 0

6x(1) - 2y{{{(dy)/(dx)}}} = 0
6x - 2y{{{(dy)/(dx)}}} = 0
    -2y{{{(dy)/(dx)}}} = -6x
       {{{(dy)/(dx)}}} = {{{(-6x)/(-2y)}}}
       {{{(dy)/(dx)}}} = {{{3x/y}}}

To use that, we must find y when x = 4

  3x² - y² = 1
3(4)² - y² = 1 
 3*16 - y² = 1
   48 - y² = 1
       -y² = -47
        y² = 47
         y = {{{"" +- sqrt(47)}}}

       {{{(dy)/(dx)}}} = {{{3x/y}}}, substitute (4,{{{"" +- sqrt(47)}}})
       {{{(dy)/(dx)}}} = {{{3(4)/("" +- sqrt(47))}}}
       {{{(dy)/(dx)}}} = {{{"" +- 12/sqrt(47)}}}

Edwin</pre>