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# Dérivées des fonctions usuelles - Formulaire

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## Fonctions puissances

Quel que soit l'entier n, left parenthesis, a, x, start superscript, n, end superscript, right parenthesis, prime, equals, a, times, n, x, start superscript, n, minus, 1, end superscript

## Fonctions racines n-ièmes

open bracket, root, start index, m, end index, close bracket, prime, equals, left parenthesis, x, start superscript, start superscript, start fraction, n, divided by, m, end fraction, end superscript, end superscript, right parenthesis, prime, equals, start fraction, n, divided by, m, end fraction, x, start superscript, start superscript, start fraction, n, divided by, m, end fraction, minus, 1, end superscript, end superscript

## Fonctions trigonométriques

open bracket, sine, left parenthesis, x, right parenthesis, close bracket, prime, equals, cosine, left parenthesis, x, right parenthesis
open bracket, cosine, left parenthesis, x, right parenthesis, close bracket, prime, equals, minus, sine, left parenthesis, x, right parenthesis
open bracket, tangent, left parenthesis, x, right parenthesis, close bracket, prime, equals, \sec, squared, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, cosine, squared, left parenthesis, x, right parenthesis, end fraction
open bracket, cotangent, left parenthesis, x, right parenthesis, close bracket, prime, equals, minus, \csc, squared, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, sine, squared, left parenthesis, x, right parenthesis, end fraction
open bracket, \sec, left parenthesis, x, right parenthesis, close bracket, prime, equals, \sec, left parenthesis, x, right parenthesis, tangent, left parenthesis, x, right parenthesis, equals, start fraction, sine, left parenthesis, x, right parenthesis, divided by, cosine, squared, left parenthesis, x, right parenthesis, end fraction
open bracket, \csc, left parenthesis, x, right parenthesis, close bracket, prime, equals, minus, \csc, left parenthesis, x, right parenthesis, cotangent, left parenthesis, x, right parenthesis, equals, minus, start fraction, cosine, left parenthesis, x, right parenthesis, divided by, sine, squared, left parenthesis, x, right parenthesis, end fraction

## Fonctions exponentielles

open bracket, left parenthesis, e, start superscript, x, end superscript, right parenthesis, close bracket, prime, equals, e, start superscript, x, end superscript
open bracket, left parenthesis, a, start superscript, x, end superscript, right parenthesis, close bracket, prime, equals, natural log, left parenthesis, a, right parenthesis, times, a, start superscript, x, end superscript

## Fonctions logarithmes

open bracket, natural log, left parenthesis, x, right parenthesis, close bracket, prime, equals, start fraction, 1, divided by, x, end fraction$\operatorname{}$
open bracket, log, start base, b, end base, left parenthesis, x, right parenthesis, close bracket, prime, equals, start fraction, 1, divided by, natural log, left parenthesis, b, right parenthesis, x, end fraction

## Fonctions trigonométriques réciproques

open bracket, \arcsin, left parenthesis, x, right parenthesis, close bracket, prime, equals, start fraction, 1, divided by, square root of, 1, minus, x, squared, end square root, end fraction
open bracket, \arccos, left parenthesis, x, right parenthesis, close bracket, prime, equals, minus, start fraction, 1, divided by, square root of, 1, minus, x, squared, end square root, end fraction
open bracket, \arctan, left parenthesis, x, right parenthesis, close bracket, prime, equals, start fraction, 1, divided by, 1, plus, x, squared, end fraction

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