derivative of x^{x^4}

Lösung

\frac{d}{d x} (x^{x^{4}})

x^{x^{4}} (4 x^{3} ln (x) + x^{3})

Schritte zur Lösung

\frac{d}{d x} (x^{x^{4}})

Wende Exponentenregel an:

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

x^{x^{4}} = e^{x^{4} l n (x)}

= \frac{d}{d x} (e^{x^{4} l n (x)})

Wende die Kettenregel an:

e^{x^{4} l n (x)} \frac{d}{d x} (x^{4} ln (x))

= e^{x^{4} l n (x)} \frac{d}{d x} (x^{4} ln (x))

\frac{d}{d x} (x^{4} ln (x)) = 4 x^{3} ln (x) + x^{3}

= e^{x^{4} l n (x)} (4 x^{3} ln (x) + x^{3})

e^{x^{4} l n (x)} = x^{x^{4}}

= x^{x^{4}} (4 x^{3} ln (x) + x^{3})

\int \frac{1}{4 + x ^{2}} d x

y^{^{''}} = x

y^{^{'}} + \frac{4}{3} y = 1 - \frac{1}{4} t

\int_{- 1}^{0} 3 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

\frac{d}{d x} (\frac{1}{π} sin (π x))