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Beliebt Rechnen >

derivative f(x)=arctan(x^{10})

Lösung

ableitung von

f (x) = arctan (x^{10})

Lösung

\frac{10 x ^{9}}{x ^{20} + 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (x^{10}))

Wende die Kettenregel an:

\frac{1}{( x ^{10} ) ^{2} + 1} \frac{d}{d x} (x^{10})

= \frac{1}{( x ^{10} ) ^{2} + 1} \frac{d}{d x} (x^{10})

\frac{d}{d x} (x^{10}) = 10 x^{9}

= \frac{1}{( x ^{10} ) ^{2} + 1} \cdot 10 x^{9}

Vereinfache

\frac{1}{( x ^{10} ) ^{2} + 1} \cdot 10 x^{9} : \frac{10 x ^{9}}{x ^{20} + 1}

= \frac{10 x ^{9}}{x ^{20} + 1}

Graph

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