scheiße

src/exercise/5.typ

@@ -0,0 +1,29 @@
+== Exercise Sheet 5 - Partial Derivatives
+
+=== Exercise 1 @Exercise[5, 1]
+#block(
+  fill: luma(230),
+  inset: 8pt,
+  radius: 4pt,
+[
+	Where is the function
+$
+	f: RR^2 -> RR
+
+	(x,y) |-> x dot sqrt(y^2 + x^2)
+$
+	partially differentiable? Calculate the first-order partial derivatives.
+])
+
+$
+g(x,y) &= x ; (delta g)/(delta x) = 1 ; (delta g)/(delta y) = 0 \
+h(x,y) &= sqrt(y^2+x^2) ; (delta h)/(delta x) = sqrt(y^2+x^2) dot 2x ; (delta h)/(delta y) = sqrt(y^2+x^2) dot 2y \
+\
+(delta f)/(delta x) &= g dot h' + g' dot h = x dot sqrt(y^2+x^2) dot 2x + 1 dot sqrt(x^2+y^2) \
+&= sqrt(x^2+y^2) (2x^2 + 1) \
+
+(delta f)/(delta y) &= g dot h' + g' dot h = x dot sqrt(x^2+y^2) dot 2y + 0 dot dots \
+&= x dot sqrt(x^2+y^2) dot 2y
+
+\ "dödö falsch"
+$

src/exercise/index.typ

@@ -5,3 +5,5 @@
 #include "3.typ"
 #pagebreak()
 #include "4.typ"
+#pagebreak()
+#include "5.typ"