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# Beweis Logarithmusregel
## Logarithmisch Differenzieren

**zz:**     $ log_a(x) = \frac 1{x * ln(a)} $

### teil 1:
##### sonderfall $ a = e $ → $ log_a = ln $
**zz:** $ ln(x) = \frac1x$

$$ e^{ln(x)} = x \ \ | \frac d{dx}$$

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## Arkustangenz ableiten

$ f(x) = tan(x) $ und $ \bar f = arctan(x)$

$$ f(\bar f(x)) = x$$

$$ \frac{\delta f(\bar f(x))}{\delta x} = \frac{\delta x}{\delta x} $$

$$ \frac{\delta tan(arctan(x))}{\delta x} = \frac{\delta x}{\delta x} $$

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#if UNITY_EDITOR
namespace Editor {
    using UnityEditor;

    [CustomEditor(typeof(MonoBehaviour), true, isFallback = true)]
    public class PositionHandleEditor : UnityEditor.Editor {
        
        void OnSceneGUI() {
            var t = target as MonoBehaviour;
            if(t == null) return;

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using System.Collections;
using UnityEngine;

// does need UnityStandardAssets > ImageEffects
// does not work if you use the ImageEffect "ScreenOverlay" on your camera for visual effects

// Usage:
// From a MonoBehaviour-Class: StartCoroutine(CameraFade.FadeOut(0.8f));
// From inside a coroutine (if you want to wait for finished fading): yield return CameraFade.FadeOut(0.5f);
// From inside a coroutine (if you dont want to wait): CameraFade.FadeOut(0.5f);

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/*
    watching this video: https://unity3d.com/learn/tutorials/modules/advanced/scripting/procedural-cave-generation-pt1
    made me scream because of this much copy-and-paste the nested-loop thing
    
    so here are a few workarounds:
*/ 

int width = 3, height = 2;
int[,] fields = new int[height, width]; // (m x n)-matrix
// ---------------------

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using UnityEngine;

public class HealthBarRenderer : MonoBehaviour {
    /// <summary>
    /// This attributes should be read from a unit's Health-Component
    /// </summary>
    [Header("Health Attributes")]
    public int Health;
    public int PhysicalShield;
    public int MagicalShield;

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using UnityEngine;
using System.Collections.Generic;
using UnityEditor;

[InitializeOnLoad]
public class MultiTransformClipboard {

    const string ComponentName = "Transform";

    static MultiTransformClipboard()

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using System.Collections.Generic;
using UnityEngine;
using UnityEngine.Events;
using UnityEngine.EventSystems;
using UnityEngine.UI;

namespace DefaultNamespace {
    public class ClickWordInTextTest : MonoBehaviour, IPointerClickHandler{
        public Text TheTextComponent; // filled in the inspector or somewhere else

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using UnityEngine;

namespace Assets.Soraphis.MiniScripts {
    public class AdditionalTextAttribute : PropertyAttribute {

        public readonly string Text;
        public AdditionalTextAttribute(string text) {
            Text = text;
        }
    }

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    /// <summary>
    /// This class uses the decorator pattern and the Idisposable interface to allow a cleaner usage of raycast/spherecasts 
    /// or other physic quarrys, which should not hit the gameobject
    /// </summary>
    class PhysicsDisposable : IDisposable {
        private static Stack<PhysicsDisposable> Pool = new Stack<PhysicsDisposable>(4);


        private List<Collider> colliders = new List<Collider>(2);
        private List<int> originalLayer;