derivative of (2x-5/((x^2+4)^3))

Lösung

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

\frac{2 ( - 5 x ^{2} + 15 x + 4 )}{( x ^{2} + 4 ) ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((x^{2} + 4)^{3}) = 6 x (x^{2} + 4)^{2}

= \frac{2 ( x ^{2} + 4 ) ^{3} - 6 x ( x ^{2} + 4 ) ^{2} ( 2 x - 5 )}{( ( x ^{2} + 4 ) ^{3} ) ^{2}}

Vereinfache

\frac{2 ( x ^{2} + 4 ) ^{3} - 6 x ( x ^{2} + 4 ) ^{2} ( 2 x - 5 )}{( ( x ^{2} + 4 ) ^{3} ) ^{2}} : \frac{2 ( - 5 x ^{2} + 15 x + 4 )}{( x ^{2} + 4 ) ^{4}}

= \frac{2 ( - 5 x ^{2} + 15 x + 4 )}{( x ^{2} + 4 ) ^{4}}

\int x (x + x^{- 1}) d x

\frac{d}{d x} (8 cos (x) sin (x))

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\int 3^{\frac{x}{2}} d x

\frac{\partial}{\partial x} (7 yz ln (x))