derivada de (tan^3(x)/3) — solución paso a paso

Derivemos:

\frac{d}{d x} (\frac{{\tan (x)}^{3}}{3})

Aplicamos la fórmula de derivación

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{n - 1}

con f =

\tan (x)

ⓘ Un factor constante se mantiene delante de la derivada: la de

k u

k \cdot u'

. La derivada de

x^{n}

n x^{n - 1}

\frac{d}{d x} (\frac{{\tan (x)}^{3}}{3})

\frac{1}{3} \cdot 3 \cdot \frac{d}{d x} (\tan (x)) \cdot {\tan (x)}^{2}

\frac{1}{3} \cdot 3 \cdot \frac{d}{d x} (\tan (x)) \cdot {\tan (x)}^{2}

ⓘ Multiplicar por 1 no cambia nada:

1 \cdot \frac{d}{d x} (\tan (x)) \cdot {\tan (x)}^{2}

\frac{d}{d x} (\tan (x)) \cdot {\tan (x)}^{2}

ⅰ

\frac{1}{3} \cdot 3

1

\frac{d}{d x} (\tan (x)) \cdot {\tan (x)}^{2}

ⓘ La derivada de

\tan (x)

\frac{1}{{\cos (x)}^{2}}

\frac{d}{d x} (\tan (x))

\frac{1}{{\cos (x)}^{2}}

\frac{1}{{\cos (x)}^{2}} \cdot {\tan (x)}^{2}

▶Derivada:

\frac{{\tan (x)}^{2}}{{\cos (x)}^{2}}