---
kurs:
  - M0065M
tags:
  - matematik
  - analys
  - envariabelanalys
  - derivata
förkunskaper:
  - "[[Derivata]]"
status: true
aliases:
  - Standardderivator
---
> **Kurs:** M0065M
> **Förkunskaper:** [[Derivata]]

---

| Funktion | Derivata |
|---|---|
| $x^n$ | $nx^{n-1}$ |
| $e^x$ | $e^x$ |
| $a^x$ | $a^x\ln a$ |
| $\ln x$ | $1/x$ |
| $\log_a x$ | $1/(x\ln a)$ |
| $\sin x$ | $\cos x$ |
| $\cos x$ | $-\sin x$ |
| $\tan x$ | $1/\cos^2 x$ |
| $\arcsin x$ | $1/\sqrt{1-x^2}$ |
| $\arccos x$ | $-1/\sqrt{1-x^2}$ |
| $\arctan x$ | $1/(1+x^2)$ |

## Läsning

- [[z.Calculus A Complete Course 10th.pdf#page=143|2.5 Derivatives of Trigonometric Functions]]
- [[z.Calculus A Complete Course 10th.pdf#page=198|3.3 The Natural Logarithm and Exponential Functions]]

## Se även

- [[Deriveringsregler]]
- [[Arcusfunktioner]]
- [[Hyperboliska funktioner]]