diff --git a/build/main.pdf b/build/main.pdf
index 7ae73db..509f813 100644
Binary files a/build/main.pdf and b/build/main.pdf differ
diff --git a/src/exercise/1.typ b/src/exercise/1.typ
index de189fc..4ce79a3 100644
--- a/src/exercise/1.typ
+++ b/src/exercise/1.typ
@@ -109,5 +109,18 @@ $
 
 #set enum(numbering: "(a)")
 + $
+  e(x) = e^x wide a(x) &= (e^x)/(1+e^x) wide b(x) = 1+e^x \
 
+  ln: RR^+ |-> RR wide e&: RR |-> RR^+ wide => f: RR |-> RR <=> DD_f = RR \
+
+  e'(x) = e(x) wide ln'(x) &= 1/x wide b'(x) = e^x \
+  a'(x) &= (b dot e' - b' dot e)/(b^2) space #text("Quotientenregel") \
+  a'(x) &= ([1+e^x] dot e^x - e^x dot e^x)/([1+e^x]^2) \
+  a'(x) &= (e^x + e^(2x) - e^(2x))/(1+2e^x+e^(2x)) = (e^x)/([1+e^x]^2) \
+
+  f'(x) &= ln'(a(x)) dot a'(x) \
+  &= 1/((e^x)/(1+e^x)) dot (e^x)/([1+e^x]^2) \
+  &= (1+e^x)/(e^x) dot (e^x)/([1+e^x]^2) \
+  &= (1+e^x)/([1+e^x]^2) \
+  &= 1/(1+e^x) checkmark
 $