derivative x/(x-8)

Lösung

ableitung von

\frac{x}{x - 8}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x - 8})

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (x - 8) = 1

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

Vereinfache

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

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

x \to 0 + lim (2 x e^{- 3 x})

\int_{0}^{16} \frac{500 x}{x ^{2} + 24} d x

d er i v a t i v e 5 π x^{2}

\frac{\partial}{\partial x} (40 x^{\frac{3}{4}} y^{\frac{1}{4}})

a re a y = x^{3}, x = - 1