Im an idiot and forgot to upload my latest. Here is to merging amirite

Author: Programatic

MultiTest2.log

@@ -1,14 +1,11 @@
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+This is pdfTeX, Version 3.14159265-2.6-1.40.19 (MiKTeX 2.9.6840 64-bit) (preloaded format=pdflatex 2018.10.28)  17 DEC 2018 21:13
 entering extended mode
- restricted \write18 enabled.
- %&-line parsing enabled.
-**MultiTest2.tex
-(./MultiTest2.tex
-LaTeX2e <2018-04-01> patch level 2
-Babel <3.18> and hyphenation patterns for 84 language(s) loaded.
-(/usr/local/texlive/2018/texmf-dist/tex/latex/base/article.cls
+**./MultiTest2.tex
+(MultiTest2.tex
+LaTeX2e <2018-04-01> patch level 5
+("D:\Users\fordm\AppData\Local\Programs\MiKTeX 2.9\tex\latex\base\article.cls"
 Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
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 File: size12.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
 )
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@@ -22,8 +19,7 @@ File: size12.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
 \abovecaptionskip=\skip41
 \belowcaptionskip=\skip42
 \bibindent=\dimen102
-)
-(./MultiTest2.aux)
+) (MultiTest2.aux)
 \openout1 = `MultiTest2.aux'.
 
 LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 8.
@@ -50,28 +46,29 @@ LaTeX Font Info:    External font `cmex10' loaded for size
 (Font)              <6> on input line 15.
  [1
 
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  1141 hyphenation exceptions out of 8191
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-
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+Output written on MultiTest2.pdf (2 pages, 77741 bytes).
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- 25 compressed objects within 1 object stream
+ 41 PDF objects out of 1000 (max. 8388607)
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MultiTest2.pdf

@@ -14,11 +14,17 @@
 \item 
 $$T(x, y, z) = x^2 +2y^2 - 3z + 1$$
 $$\Delta T  = <2x, 4y, -3>$$
-
+$$<\frac{2}{\sqrt{13}}, 0, -\frac{3}{\sqrt{13}}>$$
+\item $$T(3, 2, 1) = 15 \quad 17 = x^2 + y^2$$
+$$T(\sqrt{15},1, 1) = 15$$
+$$<\frac{3-\sqrt{15}}{\sqrt{1+(3-\sqrt{15})^2}}, \frac{1}{\sqrt{1+(3-\sqrt{15})^2}}, 0>$$
 \end{enumerate}
 
-\item $$f(x, y) = e^{2x-y-2}+y+sin(x-1) \quad x(t) = cos(5t), y(t) = sin(5t)$$
-$$f(x(t), y(t)) = e^{2cos(5t)-sin(5t)-2}+y+sin(cos(5t)-1)$$
+\item $$f(x, y) = e^{2x-y-2}+y+\sin(x-1) \quad x(t) = \cos (5t), y(t) = \sin (5t)$$
+$$\frac{df}{dt} = \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y} \frac{dy}{dt}$$
+$$\frac{\partial f}{\partial x} = 2e^{2x-y-2}+\cos(x-1) \quad \frac{dx}{dt} = -5\sin(t)$$
+$$\frac{\partial f}{\partial y} = -e^{2x-y-2}+1 \quad \frac{dy}{dt} = 5\cos(t)$$
+$$\left(2e^{2x-y-2}+\cos(x-1)\right)\cdot-5\sin(t) + \left(-e^{2x-y-2}+1\right)\cdot5\cos(t) = \frac{df}{dt}$$
 
 \item $$f(x, y) = xy + x + 2y \quad g(x, y) = xy - 4$$
 $$\Delta f = <y+1,x+2> \quad \Delta g = <y, x>$$