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Beliebt Rechnen >

derivative (6t-1)(4t-4)^{-1}

Lösung

ableitung von

(6 t - 1) (4 t - 4)^{- 1}

Lösung

- \frac{5}{4 ( t - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d t} ((6 t - 1) (4 t - 4)^{- 1})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 6 t - 1, g = (4 t - 4)^{- 1}

= \frac{d}{d t} (6 t - 1) (4 t - 4)^{- 1} + \frac{d}{d t} ((4 t - 4)^{- 1}) (6 t - 1)

\frac{d}{d t} (6 t - 1) = 6

\frac{d}{d t} ((4 t - 4)^{- 1}) = - \frac{1}{4 ( t - 1 ) ^{2}}

= 6 (4 t - 4)^{- 1} + (- \frac{1}{4 ( t - 1 ) ^{2}}) (6 t - 1)

Vereinfache

6 (4 t - 4)^{- 1} + (- \frac{1}{4 ( t - 1 ) ^{2}}) (6 t - 1) : - \frac{5}{4 ( t - 1 ) ^{2}}

= - \frac{5}{4 ( t - 1 ) ^{2}}

Graph

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