derivative y= t/((t-8)^2)

Lösung

ableitung von

y = \frac{t}{( t - 8 ) ^{2}}

\frac{- 8 - t}{( t - 8 ) ^{3}}

Schritte zur Lösung

\frac{d}{d t} (\frac{t}{( t - 8 ) ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d t}{d t} ( t - 8 ) ^{2} - \frac{d}{d t} ( ( t - 8 ) ^{2} ) t}{( ( t - 8 ) ^{2} ) ^{2}}

\frac{d t}{d t} = 1

\frac{d}{d t} ((t - 8)^{2}) = 2 (t - 8)

= \frac{1 \cdot ( t - 8 ) ^{2} - 2 ( t - 8 ) t}{( ( t - 8 ) ^{2} ) ^{2}}

Vereinfache

\frac{1 \cdot ( t - 8 ) ^{2} - 2 ( t - 8 ) t}{( ( t - 8 ) ^{2} ) ^{2}} : \frac{- 8 - t}{( t - 8 ) ^{3}}

= \frac{- 8 - t}{( t - 8 ) ^{3}}

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