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

Lösung

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

\frac{2 ( 2 x - 1 ) ^{2} ( x - 8 )}{( x - 3 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} ((2 x - 1)^{3}) = 6 (2 x - 1)^{2}

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

= \frac{6 ( 2 x - 1 ) ^{2} ( x - 3 ) ^{2} - 2 ( x - 3 ) ( 2 x - 1 ) ^{3}}{( ( x - 3 ) ^{2} ) ^{2}}

Vereinfache

\frac{6 ( 2 x - 1 ) ^{2} ( x - 3 ) ^{2} - 2 ( x - 3 ) ( 2 x - 1 ) ^{3}}{( ( x - 3 ) ^{2} ) ^{2}} : \frac{2 ( 2 x - 1 ) ^{2} ( x - 8 )}{( x - 3 ) ^{3}}

= \frac{2 ( 2 x - 1 ) ^{2} ( x - 8 )}{( x - 3 ) ^{3}}

\frac{\partial}{\partial x} (z e^{x y})

\frac{d}{d x} (\frac{1400}{( 1 + 6 e ^{- 0.02 x} )})

t a y l or f (x) = x^{- 2}

d er i v a t i v e f (x) = \frac{x}{x ^{2} + 5}

\int_{0}^{3} x^{2} e^{- x} d x