Таблица производных

Производные элементарных функций.

(C)^{'} = 0

(x^{n})^{'} = n x^{n - 1}

(e^{x})^{'} = e^{x}

(a^{x})^{'} = a^{x} ln a, a > 0, a \neq = 1

(ln x)^{'} = \frac{1}{x}, x > 0

(lo g_{a} x)^{'} = \frac{1}{x ln a}, a > 0, a \neq = 1

(sin x)^{'} = cos x

(cos x)^{'} = - sin x

(t g x)^{'} = \frac{1}{cos ^{2} x} = 1 + t g^{2} x, x \neq = \frac{π}{2} + π n

(ct g x)^{'} = - \frac{1}{sin ^{2} x} = - (1 + ct g^{2} x), x \neq = π n

(arcsin x)^{'} = - (arccos x)^{'} = \frac{1}{1 - x ^{2}}, ∣ x ∣ < 1

(arct g x)^{'} = - (arcct g x)^{'} = \frac{1}{1 + x ^{2}}

(∣ x ∣)^{'} = \frac{x}{∣ x ∣}, x \neq = 0