derivative of (3-4x/(x^2+1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 - 4 x) = - 4

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

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

Vereinfache

\frac{( - 4 ) ( x ^{2} + 1 ) - 2 x ( 3 - 4 x )}{( x ^{2} + 1 ) ^{2}} : \frac{4 x ^{2} - 6 x - 4}{( x ^{2} + 1 ) ^{2}}

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

x \to 1 - lim (2^{\frac{1}{x - 1}})

d er i v a t i v e θ sin (θ)

\frac{d y}{d x} + 7 y - 2 e^{- x} = 0

x y^{^{'}} - 2 y = 2 x^{2} ln (x)

\int y - \frac{y}{x ^{2}} e^{\frac{y}{x}} d x