derivative of (-7x^2/(2x^2-5))

Lösung

\frac{d}{d x} (\frac{- 7 x ^{2}}{2 x ^{2} - 5})

\frac{70 x}{( 2 x ^{2} - 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- 7 x ^{2}}{2 x ^{2} - 5})

Vereinfache

\frac{- 7 x ^{2}}{2 x ^{2} - 5} : - \frac{7 x ^{2}}{2 x ^{2} - 5}

= \frac{d}{d x} (- \frac{7 x ^{2}}{2 x ^{2} - 5})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - 7 \frac{d}{d x} (\frac{x ^{2}}{2 x ^{2} - 5})

Wende die Quotientenregel an:

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

= - 7 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 2 x ^{2} - 5 ) - \frac{d}{d x} ( 2 x ^{2} - 5 ) x ^{2}}{( 2 x ^{2} - 5 ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

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

= - 7 \cdot \frac{2 x ( 2 x ^{2} - 5 ) - 4 x x ^{2}}{( 2 x ^{2} - 5 ) ^{2}}

Vereinfache

- 7 \cdot \frac{2 x ( 2 x ^{2} - 5 ) - 4 x x ^{2}}{( 2 x ^{2} - 5 ) ^{2}} : \frac{70 x}{( 2 x ^{2} - 5 ) ^{2}}

= \frac{70 x}{( 2 x ^{2} - 5 ) ^{2}}

\frac{d}{d x} (- cos (5 x))

\int 7 e^{4} d x

2 y^{^{''}} + 8 y^{^{'}} + 8 y = 0

d er i v a t i v e 5 x^{4} e^{x} + e^{x} x^{5}

\frac{d}{d x} (x^{4} - 2 x^{2} - 8)