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Beliebt Rechnen >

derivative arctan((1+t)/(1-t))

Lösung

ableitung von

arctan (\frac{1 + t}{1 - t})

Lösung

\frac{1}{t ^{2} + 1}

Schritte zur Lösung

\frac{d}{d t} (arctan (\frac{1 + t}{1 - t}))

Wende die Kettenregel an:

\frac{1}{( \frac{1 + t}{1 - t} ) ^{2} + 1} \frac{d}{d t} (\frac{1 + t}{1 - t})

= \frac{1}{( \frac{1 + t}{1 - t} ) ^{2} + 1} \frac{d}{d t} (\frac{1 + t}{1 - t})

\frac{d}{d t} (\frac{1 + t}{1 - t}) = \frac{2}{( 1 - t ) ^{2}}

= \frac{1}{( \frac{1 + t}{1 - t} ) ^{2} + 1} \cdot \frac{2}{( 1 - t ) ^{2}}

Vereinfache

\frac{1}{( \frac{1 + t}{1 - t} ) ^{2} + 1} \cdot \frac{2}{( 1 - t ) ^{2}} : \frac{1}{t ^{2} + 1}

= \frac{1}{t ^{2} + 1}

Graph

Beliebte Beispiele

derivative of-2(arctan(3x-arctan(2x))+x)

\frac{d}{d x} (- 2 (arctan (3 x) - arctan (2 x)) + x)

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\int \frac{3}{60 - t} d t

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t an g e n t \frac{8}{x ^{2} + 4}

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limit as x approaches-6+of 1/((x+6)^6)

x \to - 6 + lim (\frac{1}{( x + 6 ) ^{6}})