derivative of (2x-5^{-1}*(4x+3)^{-1})

Lösung

\frac{d}{d x} ((2 x - 5)^{- 1} \cdot (4 x + 3)^{- 1})

\frac{- 16 x + 14}{( 2 x - 5 ) ^{2} ( 4 x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((2 x - 5)^{- 1} (4 x + 3)^{- 1})

Wende die Produktregel an:

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

f = (2 x - 5)^{- 1}, g = (4 x + 3)^{- 1}

= \frac{d}{d x} ((2 x - 5)^{- 1}) (4 x + 3)^{- 1} + \frac{d}{d x} ((4 x + 3)^{- 1}) (2 x - 5)^{- 1}

\frac{d}{d x} ((2 x - 5)^{- 1}) = - \frac{2}{( 2 x - 5 ) ^{2}}

\frac{d}{d x} ((4 x + 3)^{- 1}) = - \frac{4}{( 4 x + 3 ) ^{2}}

= (- \frac{2}{( 2 x - 5 ) ^{2}}) (4 x + 3)^{- 1} + (- \frac{4}{( 4 x + 3 ) ^{2}}) (2 x - 5)^{- 1}

Vereinfache

(- \frac{2}{( 2 x - 5 ) ^{2}}) (4 x + 3)^{- 1} + (- \frac{4}{( 4 x + 3 ) ^{2}}) (2 x - 5)^{- 1} : \frac{- 16 x + 14}{( 2 x - 5 ) ^{2} ( 4 x + 3 ) ^{2}}

= \frac{- 16 x + 14}{( 2 x - 5 ) ^{2} ( 4 x + 3 ) ^{2}}

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