derivative y=((t^2)/(t^3-4t))^3

Lösung

ableitung von

y = (\frac{t ^{2}}{t ^{3} - 4 t})^{3}

- \frac{3 t ^{2} ( t ^{2} + 4 )}{( t ^{2} - 4 ) ^{4}}

Schritte zur Lösung

\frac{d}{d t} ((\frac{t ^{2}}{t ^{3} - 4 t})^{3})

Wende die Kettenregel an:

3 (\frac{t ^{2}}{t ^{3} - 4 t})^{2} \frac{d}{d t} (\frac{t ^{2}}{t ^{3} - 4 t})

= 3 (\frac{t ^{2}}{t ^{3} - 4 t})^{2} \frac{d}{d t} (\frac{t ^{2}}{t ^{3} - 4 t})

\frac{d}{d t} (\frac{t ^{2}}{t ^{3} - 4 t}) = - \frac{t ^{2} + 4}{( t ^{2} - 4 ) ^{2}}

= 3 (\frac{t ^{2}}{t ^{3} - 4 t})^{2} (- \frac{t ^{2} + 4}{( t ^{2} - 4 ) ^{2}})

Vereinfache

3 (\frac{t ^{2}}{t ^{3} - 4 t})^{2} (- \frac{t ^{2} + 4}{( t ^{2} - 4 ) ^{2}}) : - \frac{3 t ^{2} ( t ^{2} + 4 )}{( t ^{2} - 4 ) ^{4}}

= - \frac{3 t ^{2} ( t ^{2} + 4 )}{( t ^{2} - 4 ) ^{4}}

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