derivative of arctan((5x/4))

Lösung

\frac{d}{d x} (arctan (\frac{5 x}{4}))

\frac{20}{25 x ^{2} + 16}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{5 x}{4}))

Wende die Kettenregel an:

\frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \frac{d}{d x} (\frac{5 x}{4})

= \frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \frac{d}{d x} (\frac{5 x}{4})

\frac{d}{d x} (\frac{5 x}{4}) = \frac{5}{4}

= \frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \cdot \frac{5}{4}

Vereinfache

\frac{1}{( \frac{5 x}{4} ) ^{2} + 1} \cdot \frac{5}{4} : \frac{20}{25 x ^{2} + 16}

= \frac{20}{25 x ^{2} + 16}

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