.MCAD 304020000 1 74 62 0
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0
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.TXT 5 13 3 0 0
Cg a61.000000,61.000000,24
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Tahoma;}}\plain\cf1\fs24 \pard {\fs32 Implicit Differentiation}}
.TXT 0 43 62 0 0
Cg a22.000000,22.000000,42
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Tahoma;}}\plain\cf1\fs24 \pard {\fs20 the input fields\par are 
highlighted\par in yellow}}
.TXT 5 -53 5 0 0
Cg a71.000000,71.000000,45
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Tahoma;}}\plain\cf1\fs24 \pard Formulate the equation in terms 
of x and y(x)}
.EQN 5 2 6 0 0
({0:x}NAME)^(2)+{0:x}NAME*{0:y}NAME({0:x}NAME)+{0:y}NAME({0:x}NAME)÷3
.TXT 5 -2 9 0 0
Cg a71.000000,71.000000,41
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Tahoma;}}\plain\cf1\fs24 \pard Then differentiate this with 
respect to x}
.EQN 6 2 10 0 1
{0:x}NAME"(({0:x}NAME)^(2)+{0:x}NAME*{0:y}NAME({0:x}NAME)+{0:y}NAME({0:x}NAME)÷3){63}2*{0:x}NAME+{0:y}NAME({0:x}NAME)+{0:x}NAME*{0:x}NAME"{0:y}NAME({0:x}NAME)+{0:x}NAME"{0:y}NAME({0:x}NAME)÷0
.TXT 8 0 19 0 0
Cg a69.000000,69.000000,58
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Tahoma;}}\plain\cf1\fs24 \pard We solve this for y', using the 
"Given ... Find()" command}
.EQN 5 10 34 0 0
{0:Given}NAME
.EQN 4 0 35 0 1
{0:x}NAME"(({0:x}NAME)^(2)+{0:x}NAME*{0:y}NAME({0:x}NAME)+{0:y}NAME({0:x}NAME)÷3)
.EQN 6 0 36 0 0
{0:Find}NAME({0:x}NAME"{0:y}NAME({0:x}NAME)){63}(-(2*{0:x}NAME+{0:y}NAME({0:x}NAME)))/(({0:x}NAME+1))
.TXT 8 -10 37 0 0
Cg a69.000000,69.000000,115
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Tahoma;}}\plain\cf1\fs24 \pard We can try to check the formula 
by trying to solve our equation\par first for y(x), and the 
differentiating the result:}
.EQN 7 10 54 0 0
{0:Given}NAME
.EQN 4 0 55 0 1
({0:x}NAME)^(2)+{0:x}NAME*{0:y}NAME({0:x}NAME)+{0:y}NAME({0:x}NAME)÷3
.EQN 4 0 56 0 0
{0:Find}NAME({0:y}NAME({0:x}NAME)){63}(-(({0:x}NAME)^(2)-3))/(({0:x}NAME+1))
.TXT 0 19 60 0 0
Cg a39.000000,39.000000,9
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Tahoma;}}\plain\cf1\fs24 \pard , that is}
.EQN 0 11 57 0 1
{0:f}NAME({0:x}NAME):(-(({0:x}NAME)^(2)-3))/(({0:x}NAME+1))
.EQN 8 0 58 0 0
{0:x}NAME"{0:f}NAME({0:x}NAME){63}-2*({0:x}NAME)/(({0:x}NAME+1))-((-({0:x}NAME)^(2)+3))/((({0:x}NAME+1))^(2))