Vzorec  podmienky platnosti  Vzorec  podmienky platnosti
[c]′ = 0, x∈R, c∈R  [x]′ = 1, x∈R
[xn]′ = nxn−1, x∈R, n∈N  [xa]′ = axa−1, x > 0, a∈R
[ex]′ = ex, x∈R  [ax]′ = ax lna, x∈R, a > 0
[lnx]′ = \frac{1}{x}, x > 0  [loga x]′ = \frac{1}{x lna}, x > 0, a > 0, a≠1
[ln|x|]′ = \frac{1}{x}, x≠0  [loga |x|]′ = \frac{1}{x lna}, x≠0, a > 0, a≠1
[sinx]′ = cosx, x∈R  [cosx]′ = − sinx, x∈R
[tgx]′ = \frac{1}{cos^{2} x}, x≠(2k+1)\frac{π}{2}, k ∈Z  [cotgx]′ = −\frac{1}{sin^{2} x}, x≠kπ, k ∈Z
[arcsinx]′ = \frac{1}{\sqrt{1−x^{2}}} , x∈(−1 ; 1)  [arccosx]′ = −\frac{1}{\sqrt{1−x^{2}}} , x∈(−1 ; 1)
[arctgx]′ = \frac{1}{1+x^{2}} , x∈R  [arccotgx]′ = −\frac{1}{1+x^{2}} , x∈R

[sinhx]′ = coshx, x∈R [coshx]′ = sinhx, x∈R

[tghx]′ = \frac{1}{cosh^{2} x}, x∈R

[cotghx]′ = −\frac{1}{sinh^{2} x}, x≠0
[argsinhx]′ = \frac{1}{\sqrt{x^{2}+1}} , x∈R  [argcoshx]′ = \frac{1}{\sqrt{x^{2}−1}}, x > 1

[argtghx]′ = \frac{1}{1−x^{2}} , x∈(−1 ; 1)

[argcotghx]′ = \frac{1}{1−x^{2}} , x∈R − ⟨−1 ; 1⟩

Derivácie základných elementárnych funkcií.