derivative of (8sqrt(x)+1/(x^{-5)})

Lösung

\frac{d}{d x} (\frac{8 x + 1}{x ^{- 5}})

x^{4} (44 x + 5)

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x + 1}{x ^{- 5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x + 1 ) x ^{- 5} - \frac{d}{d x} ( x ^{- 5} ) ( 8 x + 1 )}{( x ^{- 5} ) ^{2}}

\frac{d}{d x} (8 x + 1) = \frac{4}{x}

\frac{d}{d x} (x^{- 5}) = - \frac{5}{x ^{6}}

= \frac{\frac{4}{x} x ^{- 5} - ( - \frac{5}{x ^{6}} ) ( 8 x + 1 )}{( x ^{- 5} ) ^{2}}

Vereinfache

\frac{\frac{4}{x} x ^{- 5} - ( - \frac{5}{x ^{6}} ) ( 8 x + 1 )}{( x ^{- 5} ) ^{2}} : x^{4} (44 x + 5)

= x^{4} (44 x + 5)

\int x^{n + 2} d x

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\frac{d y}{d x} = 4 y e^{x + 4}