Derivadas

(cod: P-49-28-5) A continuación se presentan afirmaciones relacionadas con la derivada de diversas funciones:

(1) Si \(c \in \mathbb{R}\), \(\dfrac{d}{dx}\left(c\right) = 0.\)

(2) Si \(c \in \mathbb{R}\), \(\dfrac{d}{dx}\left(cx\right) = cx\)

(3) Si \(n \in \mathbb{N}\), \(\dfrac{d}{dx}\left(x^n \right) = nx^{n-1}\)

(4) \(\dfrac{d}{dx}\left(x^{1/2}\right) = \frac{1}{2} x^{1/2 - 1} = \dfrac{1}{2\sqrt{x}}\)

(5) Si \(n \in \mathbb{N}\), \(\dfrac{d}{dx}\left(x^{-n} \right) = nx^{-n-1}\)

(6) \(\dfrac{d}{dx}\left(\text{sen}(x) \right)= \cos(x) \)

(7) \(\dfrac{d}{dx}\left(\cos(x)\right)= \text{sen}(x)\)

(8) \(\dfrac{d}{dx}\left(\tan(x)\right) = \sec^2(x)\)

(9) \(\dfrac{d}{dx}\left(\sec(x)\right) = \tan^2(x)\)

(10) \(\dfrac{d}{dx}\left(b^x \right) = b^x \ln(b)\)

(11) Si \(0 < b \ne 1\), \(\dfrac{d}{dx}\left(\log_b(x)\right) = \dfrac{1}{x}\)

(12) \(\dfrac{d}{dx}\left(e^x\right) = e^x\)

(13) \(\dfrac{d}{dx}\left(\ln(x)\right) = \dfrac{1}{x}\)

(14) \(\dfrac{d}{dx}\left(3^x\right) = x 3^{x-1}\)

Podemos afirmar que: