derivative of (x^2/(x-6))

Lösung

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

\frac{x ^{2} - 12 x}{( x - 6 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x ( x - 6 ) - 1 \cdot x ^{2}}{( x - 6 ) ^{2}} : \frac{x ^{2} - 12 x}{( x - 6 ) ^{2}}

= \frac{x ^{2} - 12 x}{( x - 6 ) ^{2}}

\frac{\partial}{\partial x} (\frac{x y}{1 + x y ^{2}})

\frac{d}{d x} (a e^{2 x} + b e^{x})

\frac{\partial}{\partial z} (e^{x} sin (yz))

\int 10 sin^{3} (x) cos^{7} (x) d x

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