Matematika - limity + derivace

test 1 VŠCHT první semestr

f(x) = c

f´(x) = 0

f(x) = aⁿ

f´(x) = n×aⁿ⁻¹

f(x) = eⁿ

f´(x) = eⁿ

f(x) = ln x

f´(x) = 1/x

f(x) = sin x

f´(x) = cos x

f(x) = cos x

f´(x) = -sin x

f(x) = tg x

f´(x) = 1/cos² x

f(x) = cotg x

f´(x) = -1/sin² x

f(x) = arcsin x

f´(x) = 1/√1-x²

f(x) = arccos x

f´(x) = -1/√1-x²

f(x) = arctgx

f´(x) = 1/1+x²

f(x) = arccotg x

f´(x) = -1/1+x²

f(x) = x²

f´(x) = 2x

f(x) = x³

f´(x) = 3x²

f(x) = 1/x

f´(x) = -1/x²

f(x) = x

f´(x) = 1

f(x) = √x

f´(x) = 1/2√x

součin konstanta

kostanta×f´(x)

funkce ± funkce

f´(x) ± g´(x)

součin 2 funkce

f´×g + f×g´

podíl 2 funkce

f´×g-f×g´/ g²

L´hospitalovo pravidlo

limita f(x)/g(x) = lim f´(x)/gˇ(x)

neurčité výrazy

0/0, ∞/∞, ∞-∞, 0-∞, 0⁰, ∞⁰, 1ⁿekonečno

c/∞=

0

eⁿekonečno

∞

ln 1

0

ln e

1

sin x = 0

x = 0

sin x = π/6

x = ½

sin x = π/4

x = √2/2

sin x = π/3

x = √3/2

sin x = π/2

x = 1

cos x = 0

x = 1

cos x = π/6

x = √3/2

cos x = π/4

x = √2/2

cos x = π/3

x = ½

cos x = π/2

x = 0

tg x = 0

x = 0

cotg x = 0

x = není def.

tg x = π/6

x = √3/3

cotg x = π/6

√3

tg x = π/4

x = 1

cotg x = π/4

x = 1

tg x = π/3

x = √3

cotg x = π/3

x = √3/3

tg x = π/2

x = není def.

cotg x = π/2

x = 0