Tahák - derivace a integrály

Derivace:

ƒ´(c)=lim n→0 [ƒ(c+h)- ƒ(c)]/h

(f/g)´= (f´g-fg´)/g2

(fg)´= f´g+fg´

[f(g)]´=f´(g)g´

(xa)´=nxn-1

(xx)´=xx(ln x + 1)

(cos x)´= - sin x

(sin x)´=cos x

(tg x)´=1/cos2 x

(cotg x)´= - 1/sin2 x

(arcsin x)´= 1/√(1-x2)

(arccos x)´= - 1/√(1-x2)

(ln x)´=1/x

(ex)´=ex

x

0

∏/6

∏/4

∏/3

∏/2

sin x

0

1/2

√2/2

√3/2

1

cos x

1

√3/2

√2/2

1/2

0

tg x

0

√3/2

1

√3

ned.

cotg x

ned.

√3

1

√3/2

0

x

-1

-√3/2

-√2/2

-1/2

0

arcsin x

-∏/2

-∏/3

-∏/4

-∏/6

0

arccos x

∏

5∏/6

3∏/4

2∏/3

∏/2

Integrály: fce F je primitivní k ƒ v I, platí-li F´(x) = ƒ(x) pro každé x z I.

∫ cos x dx = sin x +c

∫ sin x dx = - cos x + c

∫ 1/(1+x2) dx = arctg x +c

∫ 1/(1+x2) dx = - arccotg x + c

∫ xn dx = (xn+1)/(n+1) + c

n∈N

∫ 0 dx = c

∫ 1 dx = x + c

∫ ax dx = ax/ln a + c

a ≠ 1, a • 0

∫ ex dx = ex +c

∫ 1/x dx = ln ⎮x⎮