improving the derived state section to fix #489 (#539)

Co-authored-by: Sarah <gerrardsarah@gmail.com>
Co-authored-by: Atila Fassina <atila@fassina.eu>

src/routes/guides/state-management.mdx

@@ -121,7 +121,7 @@ function Counter() {
 	};
 
 	createEffect(() => {
-		setDoubleCount(count() * 2); // Update doubleCount whenever count changes
+		setDoubleCount((prev) => prev * 2); // Update doubleCount whenever count changes
 	});
 
 	return (
@@ -140,6 +140,8 @@ Here, a side-effect refers to operations or updates that affect state outside of
 In the `Counter` component, a `createEffect` function can be used to update the `doubleCount` state whenever the `count` state changes.
 This keeps the `doubleCount` state in sync with the `count` state, and allows the UI to display the doubled value of `count` to the user.
 
+View this example of [`doubleCount` in a `createEffect` in the Solid Playground example](https://playground.solidjs.com/anonymous/b05dddaa-e62a-4c56-b745-5704f3a40194).
+
 <TabsCodeBlocks>
 <div id="First render">
 	```html title="Counter.tsx" Current count: 0 Doubled count: 0 ```
@@ -153,31 +155,29 @@ This keeps the `doubleCount` state in sync with the `count` state, and allows th
 ## Derived state
 
 When you want to calculate new state values based on existing state values, you can use derived state.
-Derived state is state that is calculated from other state values.
 This is a useful pattern when you want to display a transformation of a state value to the user, but do not want to modify the original state value or create a new state value.
 
-Derived values can be created through using a signal within a function, which can be referred to as a [derived signal](/concepts/derived-values/derived-signals):
+Derived values can be created using a signal within a function, which can be referred to as a [derived signal](/concepts/derived-values/derived-signals).
 
-```jsx
-import { createSignal } from "solid-js";
+This approach can be used to simplify the `doubleCount` example above, where the additional signal and effect can be replaced with a derived signal:
+
+```jsx del={5, 11-13} ins={15}
+import { createSignal } from "solid-js"
 
 function Counter() {
 	const [count, setCount] = createSignal(0);
 	const [doubleCount, setDoubleCount] = createSignal(0);
 
-	// Derived signal
-	const squaredCount = () => {
-		return count() * count();
-	};
-
 	const increment = () => {
 		setCount((prev) => prev + 1);
 	};
 
 	createEffect(() => {
-		setDoubleCount(count() * 2); // Update doubleCount whenever count changes
+		setDoubleCount((prev) => prev * 2); // Update doubleCount whenever count changes
 	});
 
+	const doubleCount = () => count() * 2
+
 	return (
 		<>
 			<div>Current count: {count()}</div>
@@ -188,44 +188,95 @@ function Counter() {
 }
 ```
 
-While this approach works, it can be inefficient as the `doubleCount` signal will be re-evaluated on every render.
-When a function is computationally expensive, or used multiple times within a component, this can lead to performance issues.
-To avoid this, Solid introduced [Memos](/concepts/derived-values/memos):
+While this approach works for simple use cases, if `doubleCount` is used several times within a component or contains a computationally expensive calculation, it can lead to performance issues.
 
-```jsx
-import { createSignal, createEffect, createMemo } from "solid-js";
+The derived signal would be re-evaluated not just each time `count` is changed, but also for each use of `doubleCount()`.
+
+```jsx del={10} ins={11-14, 20-21}
+import { createSignal } from "solid-js"
 
 function Counter() {
-	const [count, setCount] = createSignal(0);
-	const [doubleCount, setDoubleCount] = createSignal(0);
+	const [count, setCount] = createSignal(0)
 
-	// Memo
-	const squaredCount = createMemo(() => count() * count());
+	const increment = () => {
+		setCount(count() + 1)
+	}
+
+	const doubleCount = () => count() * 2
+	const doubleCount = () => {
+		console.log('doubleCount called')
+		return count() * 2
+	}
+
+	return (
+		<>
+			<div>Current count: {count()}</div>
+			<div>Doubled count: {doubleCount()}</div>
+			<div>Doubled count: {doubleCount()}</div>
+			<div>Doubled count: {doubleCount()}</div>
+			<button onClick={increment}>Increment</button>
+		</>
+	)
+}
+```
+
+```shellsession title="Console output"
+doubleCount called
+doubleCount called
+doubleCount called
+```
+
+For cases like this, you can use [Memos](/concepts/derived-values/memos) to store the value of `doubleCount`, which are also referred to as a memoized or cached value. 
+When using a memo, the calculation will only run **once** when the value of `count` changes and can be accessed multiple times without re-evaluating for each additional use.
+
+Using the [`createMemo`](/reference/basic-reactivity/create-memo) function, you can create a memoized value:
+
+```jsx ins={15-18, 26-28} ins=", createMemo"
+import { createSignal, createMemo } from "solid-js"
+
+function Counter() {
+	const [count, setCount] = createSignal(0)
 
 	const increment = () => {
 		setCount((prev) => prev + 1);
 	};
 
 	const doubleCount = () => {
-		return count() * 2;
-	};
+		console.log('doubleCount called')
+		return count() * 2
+	}
+
+	const doubleCountMemo = createMemo(() => {
+		console.log('doubleCountMemo called')
+		return count() * 2
+	})
 
 	return (
 		<>
+			<div>Current count: {count()}</div>
+			<div>Doubled count: {doubleCount()}</div>
+			<div>Doubled count: {doubleCount()}</div>
+			<div>Doubled count: {doubleCount()}</div>
+			<div>Doubled count: {doubleCountMemo()}</div>
+			<div>Doubled count: {doubleCountMemo()}</div>
+			<div>Doubled count: {doubleCountMemo()}</div>
 			<button onClick={increment}>Increment</button>
-			<div>
-				<div>Current count: {count()}</div>
-				<div>Doubled count: {doubleCount()}</div>
-				<div>Squared count: {squaredCount()}</div>
-			</div>
 		</>
 	);
 }
 ```
 
-Using the [`createMemo`](/reference/basic-reactivity/create-memo) function, you can create a memoized value that is only re-evaluated when its dependencies change.
-This means that the value of `squaredCount` will only be re-evaluated when the value of `count` changes.
-This is a more efficient approach to calculating derived state, as it only re-evaluates the memoized value when necessary.
+```shellsession title="Console output"
+doubleCountMemo called
+doubleCount called
+doubleCount called
+doubleCount called
+```
+
+While accessed multiple times, the `doubleCountMemo` will only re-evaluate and log once.
+This is different from the derived signal, `doubleCount`, which is re-evaluated for each time it is accessed.
+
+View a similar [example comparing a derived signal and a memo in the Solid Playground](https://playground.solidjs.com/anonymous/288736aa-d5ba-45f7-a01f-1ac3dcb1b479).
 
 ## Lifting state
 
@@ -244,7 +295,7 @@ function App() {
 	const squaredCount = createMemo(() => count() * count());
 
 	createEffect(() => {
-		setDoubleCount(count() * 2);
+		setDoubleCount((prev) => prev * 2);
 	});
 
 	return (