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

Lösung

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

\frac{2 x ( x + 2 ) ^{3} ( - 8 x ^{2} - 3 x - 2 )}{( 2 x ^{2} - 1 ) ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((2 x^{2} - 1)^{3}) = 12 x (2 x^{2} - 1)^{2}

= \frac{( 2 x ( x + 2 ) ^{4} + 4 ( x + 2 ) ^{3} x ^{2} ) ( 2 x ^{2} - 1 ) ^{3} - 12 x ( 2 x ^{2} - 1 ) ^{2} x ^{2} ( x + 2 ) ^{4}}{( ( 2 x ^{2} - 1 ) ^{3} ) ^{2}}

Vereinfache

\frac{( 2 x ( x + 2 ) ^{4} + 4 ( x + 2 ) ^{3} x ^{2} ) ( 2 x ^{2} - 1 ) ^{3} - 12 x ( 2 x ^{2} - 1 ) ^{2} x ^{2} ( x + 2 ) ^{4}}{( ( 2 x ^{2} - 1 ) ^{3} ) ^{2}} : \frac{2 x ( x + 2 ) ^{3} ( - 8 x ^{2} - 3 x - 2 )}{( 2 x ^{2} - 1 ) ^{4}}

= \frac{2 x ( x + 2 ) ^{3} ( - 8 x ^{2} - 3 x - 2 )}{( 2 x ^{2} - 1 ) ^{4}}

l a pl a ce t r an s f or m sin (t - 8)

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

\frac{d}{d x} (6 x^{2} sin (x) tan (x))

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

\frac{\partial}{\partial x} (sin (2 x + y) sin (y))