derivative of (x^2/(9+8x))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{9 + 8 x})

\frac{18 x + 8 x ^{2}}{( 9 + 8 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{9 + 8 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 9 + 8 x ) - \frac{d}{d x} ( 9 + 8 x ) x ^{2}}{( 9 + 8 x ) ^{2}}

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

\frac{d}{d x} (9 + 8 x) = 8

= \frac{2 x ( 9 + 8 x ) - 8 x ^{2}}{( 9 + 8 x ) ^{2}}

Multipliziere aus

2 x (9 + 8 x) - 8 x^{2} : 18 x + 8 x^{2}

= \frac{18 x + 8 x ^{2}}{( 9 + 8 x ) ^{2}}

x \to 0 lim (x^{4} sin (\frac{1}{x}))

in v erse l a pl a ce \frac{s + 2}{s + 3}

\frac{d}{d x} (x^{5} + 5 x^{4} - 10 x^{2} + 6)

im pl i c i t \frac{d y}{d x}, 2 x^{4} + 9 y = 2 x^{2} y + 36

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