podmienky platnosti
Vzorec
[c]′ = 0,
[ex ]′ = ex , [ln x]′ =
x ∈ R, n ∈ N
[sin x]′ = cos x,
[arctg x]′ =
x 6= (2k+1) π2 , k ∈ Z
1 , 1+x2
[sinh x]′ = cosh x, [tgh x]′ =
1 , cosh2 x
[argsinh x]′ = [argtgh x]′ =
x ∈ (−1 ; 1) x∈R x∈R
1 , 1−x2
x > 0, a > 0, a 6= 1
1 , x ln a
x 6= 0, a > 0, a 6= 1 x∈R
[cotg x]′ = − sin12 x ,
x 6= kπ, k ∈ Z
1 [arccos x]′ = − √1−x , 2
x ∈ (−1 ; 1)
1 [arccotg x]′ = − 1+x 2,
x∈R
[cosh x]′ = sinh x,
x∈R
[cotgh x]′ = − sinh1 2 x ,
x∈R
√ 1 , x2 +1
x ∈ R, a > 0
[cos x]′ = − sin x,
x∈R
√ 1 , 1−x2
[arcsin x]′ =
x > 0, a ∈ R
1 , x ln a
[loga |x|]′ =
x 6= 0
1 , cos2 x
x∈R
[xa]′ = axa−1,
[loga x]′ =
x>0
1 , x
podmienky platnosti
[ax ]′ = ax ln a,
x∈R
1 , x
[ln |x|]′ = [tg x]′ =
[x]′ = 1,
x ∈ R, c ∈ R
[xn]′ = nxn−1,
Vzorec
x∈R x ∈ (−1 ; 1)
[argcosh x]′ =
√ 1 , x2 −1
[argcotgh x]′ =
Derivácie základných elementárnych funkcií.
1 , 1−x2
x 6= 0 x>1
x ∈ R − h−1 ; 1i