Question 1209241
<pre>
QUOTIENT RULE:

{{{matrix(1,3,

y,""="",((TOP))/((BOTTOM)))}}}

{{{matrix(1,3,
dy/dx,""="",((BOTTOM)*(matrix(1,3,DERIVATIVE,OF,TOP))-(TOP)*(matrix(1,3,DERIVATIVE,OF,BOTTOM))^"")/((BOTTOM)^2)     )}}} 

EXAMPLE:

{{{matrix(1,3,

y,""="",(2x^2+3x+1)/(5x+1^""))}}}

{{{matrix(1,3,
dy/dx,""="",((5x+1^"")*(4x+3^"")-(2x^2+3x+1)*(5^""))/((5x+1^"")^2)     )}}}

Simplify that and get:

{{{matrix(1,3,
dy/dx,""="",(2(5x^2-2x-1))/((5x+1^"")^2)     )}}}

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POWER RULE:

{{{matrix(1,3,

y,""="",(BASE)^((EXPONENT)))}}}
{{{matrix(1,3,
dy/dx,""="",(EXPONENT)*(BASE)^((EXPONENT-1))*(matrix(1,3,DERIVATIVE,OF,BASE)))}}} 

Example:

{{{matrix(1,3,

y,""="",(4x^2+1)^3))}}}
{{{matrix(1,3,
dy/dx,""="",3*(4x^2+1)^2*(8x))}}}
{{{matrix(1,3,
dy/dx,""="",24x*(4x^2+1)^2)}}}

Edwin</pre>