derivative of ln(1+x^4)

Lösung

\frac{d}{d x} (ln (1 + x^{4}))

\frac{4 x ^{3}}{1 + x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (ln (1 + x^{4}))

Wende die Kettenregel an:

\frac{1}{1 + x ^{4}} \frac{d}{d x} (1 + x^{4})

= \frac{1}{1 + x ^{4}} \frac{d}{d x} (1 + x^{4})

\frac{d}{d x} (1 + x^{4}) = 4 x^{3}

= \frac{1}{1 + x ^{4}} \cdot 4 x^{3}

Vereinfache

\frac{1}{1 + x ^{4}} \cdot 4 x^{3} : \frac{4 x ^{3}}{1 + x ^{4}}

= \frac{4 x ^{3}}{1 + x ^{4}}

\int_{4}^{\infty} e^{- \frac{y}{2}} d y

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