derivative of x^{\sqrt[3]{ln(x}})

Lösung

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

x^{3 l n (x)} (\frac{ln ^{\frac{1}{3}} ( x )}{3 x} + \frac{3 ln ( x )}{x})

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{3 l n (x)} = e^{3 l n (x) l n (x)}

= \frac{d}{d x} (e^{3 l n (x) l n (x)})

Wende die Kettenregel an:

e^{3 l n (x) l n (x)} \frac{d}{d x} (3 ln (x) ln (x))

= e^{3 l n (x) l n (x)} \frac{d}{d x} (3 ln (x) ln (x))

\frac{d}{d x} (3 ln (x) ln (x)) = \frac{ln ^{\frac{1}{3}} ( x )}{3 x} + \frac{3 ln ( x )}{x}

= e^{3 l n (x) l n (x)} (\frac{ln ^{\frac{1}{3}} ( x )}{3 x} + \frac{3 ln ( x )}{x})

e^{3 l n (x) l n (x)} = x^{3 l n (x)}

= x^{3 l n (x)} (\frac{ln ^{\frac{1}{3}} ( x )}{3 x} + \frac{3 ln ( x )}{x})

\int - \frac{2}{3} y^{- \frac{4}{3}} d y

y = \frac{3 cos ( x )}{1 + sin ( x )}

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

\int_{0}^{l n (3)} e^{x} d x

\int e^{c o s (40 t)} sin (40 t) d t