Formulaire des dérivées

Question 1

$(k)'$

Accepted Answer

$0$

Question 2

$(x^\alpha)'$

Accepted Answer

$\alpha x^{\alpha-1}$

Question 3

$\left(\frac{1}{x}\right)'$

Accepted Answer

$-\frac{1}{x^2}$

Question 4

$\left(\sqrt{x}\right)'$

Accepted Answer

$\frac{1}{2\sqrt{x}}$

Question 5

$(e^{\alpha x})'$

Accepted Answer

$\alpha e^{\alpha x}$

Question 6

$(ln(x))'$

Accepted Answer

$\frac{1}{x}$

Question 7

$(cos(x))'$

Accepted Answer

$-sin(x)$

Question 8

$(sin(x))'$

Accepted Answer

$cos(x)$

Question 9

$(tan(x))'$

Accepted Answer

$\frac{1}{cos^2(x)} = 1 + tan^2(x)$

Question 10

$(arccos(x))'$

Accepted Answer

$-\frac{1}{\sqrt{1 - x^2}}$

Question 11

$(arcsin(x))'$

Accepted Answer

$\frac{1}{\sqrt{1 - x^2}}$

Question 12

$(arctan(x))'$

Accepted Answer

$\frac{1}{1 + x^2}$

Question 13

$(ch(x))'$

Accepted Answer

$sh(x)$

Question 14

$(sh(x))'$

Accepted Answer

$ch(x)$

Question 15

$(th(x))'$

Accepted Answer

$\frac{1}{ch^2(x)} = 1 - th^2(x)$

Question 16

$((v \circ u)(x))'$

Accepted Answer

$u'(x) 	imes v'(u(x))$

Question 17

$(u(ax + b))'$

Accepted Answer

$a 	imes u'(ax + b)$

Question 18

$(u^\alpha(x))'$

Accepted Answer

$\alpha 	imes u'(x) 	imes u^{\alpha - 1}(x)$

Question 19

$\left(\frac{1}{u(x)}\right)'$

Accepted Answer

$-\frac{u'(x)}{u^2(x)}$

Question 20

$\left(\frac{u(x)}{v(x)}\right)'$

Accepted Answer

$\frac{u'(x)v(x) - v'(x)u(x) }{v^2(x)}$

Question 21

$(u(x) 	imes v(x))'$

Accepted Answer

$u'(x)v(x) + v'(x)u(x)$

Question 22

$\left(\sqrt{u(x)}\right)'$

Accepted Answer

$\frac{u'(x)}{2\sqrt{u(x)}}$

Question 23

$(e^{u(x)})'$

Accepted Answer

$u'(x)e^{u(x)}$

Question 24

$ln(u(x))$

Accepted Answer

$\frac{u'(x)}{u(x)}$

Formulaire des dérivées

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