Производная функции

Правила дифференцирования

(u ± v)′ = u′ ± v′

(u ⋅ v)′ = u′v + uv′

${\left(\frac{u}{v}\right)}^{\prime }=\frac{u^{\prime }v-u{v}^{\prime }}{v^2}$

(u(v(x)))′ = u′ ⋅ v′(x)

Уравнение касательной к графику

y = f ′(x₀) ⋅ (x − x₀) + f (x₀)

k = f ′(x₀)

c′ = 0

(cx)′ = c

(xⁿ)′ = n x^{n − 1}

$\left(\sqrt{x}\right)\prime =\frac{1}{2\sqrt{x}}$

(a^x)′ = a^x lna

(e^x)′ = e^x

(log_ax)′ = $\frac{1}{x\text{ln}a}$

(lnx)′ = $\frac{1}{x}$

(sin x)′ = cos x

(cos x)′ = − sin x

(tg x)′ = $\frac{1}{{\text{cos}}^{2}x}$

(ctg x)′ = $-\frac{1}{{\text{sin}}^{2}x}$

$\left(\text{arcsin}x\right)\prime =\frac{1}{\sqrt{1-x^2}}$

$\left(\text{arccos}x\right)\prime =-\frac{1}{\sqrt{1-x^2}}$

$\left(\text{arctg}x\right)\prime =\frac{1}{1+x^2}$

$\left(\text{arcctg}x\right)\prime =-\frac{1}{1+x^2}$