derivative y=tan(t/(1+t^2))

Lösung

ableitung von

y = tan (\frac{t}{1 + t ^{2}})

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int_{0}^{1} 4 π (x^{2} - x^{10}) d x

t an g e n t \frac{3}{x}

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