derivative of (A+Bx+Cx^2/(x^2))

Lösung

\frac{d}{d x} (\frac{A + B x + C x ^{2}}{x ^{2}})

\frac{- B x - 2 A}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{A + B x + C x ^{2}}{x ^{2}})

Behandle

A, B, C

als Konstanten

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( A + B x + C x ^{2} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( A + B x + C x ^{2} )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (A + B x + C x^{2}) = 2 C x + B

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

= \frac{( 2 C x + B ) x ^{2} - 2 x ( A + B x + C x ^{2} )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{( 2 C x + B ) x ^{2} - 2 x ( A + B x + C x ^{2} )}{( x ^{2} ) ^{2}} : \frac{- B x - 2 A}{x ^{3}}

= \frac{- B x - 2 A}{x ^{3}}

\frac{d}{d x} (x e^{x y})

\frac{\partial}{\partial x} (4 e^{x} - 2 x e^{y})

d er i v a t i v e ln (u)

\int \frac{x ^{6}}{1 + x ^{2}} d x

\int x (x^{2} - 8)^{3} d x