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

Derivemos:

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

Utilizamos la fórmula de derivación

\frac{d}{d x} (\ln (f)) = \frac{d}{d x} (f) \cdot \frac{1}{f}

con f =

\tan (x^{3})

ⓘ La derivada de

\ln (x)

\frac{1}{x}

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

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

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

Aplicamos la fórmula de derivación

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

con f =

x^{3}

ⓘ Multiplicar una fracción por un término equivale a multiplicar su numerador:

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

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

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

■La derivada de

\tan (x)

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

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

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

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

ⓘ La derivada de

x^{n}

n x^{n - 1}

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

3 x^{2}

\frac{\frac{3 x^{2}}{{\cos (x^{3})}^{2}}}{\tan (x^{3})}

ⓘ Dividir una fracción por

\tan (x^{3})

equivale a multiplicar su denominador por

\tan (x^{3})

\frac{\frac{3 x^{2}}{{\cos (x^{3})}^{2}}}{\tan (x^{3})}

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

▶Derivada:

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