diff --git a/src/runtime/store/index.ts b/src/runtime/store/index.ts
index afd4ccabd61e..51a13b85e21f 100644
--- a/src/runtime/store/index.ts
+++ b/src/runtime/store/index.ts
@@ -13,7 +13,7 @@ export type Updater<T> = (value: T) => T;
 type Invalidator<T> = (value?: T) => void;
 
 /** Start and stop notification callbacks. */
-export type StartStopNotifier<T> = (set: Subscriber<T>, update?: (fn: Updater<T>) => void) => Unsubscriber | void;
+export type StartStopNotifier<T> = (set: Subscriber<T>, update: (fn: Updater<T>) => void) => Unsubscriber | void;
 
 /** Readable interface for subscribing. */
 export interface Readable<T> {
@@ -115,6 +115,20 @@ type Stores = Readable<any> | [Readable<any>, ...Array<Readable<any>>] | Array<R
 type StoresValues<T> = T extends Readable<infer U> ? U :
 	{ [K in keyof T]: T[K] extends Readable<infer U> ? U : never };
 
+/**
+ * Derived value store by synchronizing one or more readable stores and
+ * applying an aggregation function over its input values.
+ *
+ * @param stores - input stores
+ * @param fn - function callback that aggregates the values
+ * @param initial_value - when used asynchronously
+ */
+ export function derived<S extends Stores, T>(
+	stores: S,
+	fn: (values: StoresValues<S>, set: Subscriber<T>, update: (fn: Updater<T>) => void) => Unsubscriber | void,
+	initial_value?: T
+): Readable<T>;
+
 /**
  * Derived value store by synchronizing one or more readable stores and
  * applying an aggregation function over its input values.
@@ -125,7 +139,7 @@ type StoresValues<T> = T extends Readable<infer U> ? U :
  */
 export function derived<S extends Stores, T>(
 	stores: S,
-	fn: (values: StoresValues<S>, set: Subscriber<T>, update?: (fn: Updater<T>) => void) => Unsubscriber | void,
+	fn: (values: StoresValues<S>, set: Subscriber<T>) => Unsubscriber | void,
 	initial_value?: T
 ): Readable<T>;