derivative (x^2+5)/x

Lösung

ableitung von

\frac{x ^{2} + 5}{x}

\frac{x ^{2} - 5}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 5}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 5 ) x - \frac{d x}{d x} ( x ^{2} + 5 )}{x ^{2}}

\frac{d}{d x} (x^{2} + 5) = 2 x

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

= \frac{2 xx - 1 \cdot ( x ^{2} + 5 )}{x ^{2}}

Vereinfache

\frac{2 xx - 1 \cdot ( x ^{2} + 5 )}{x ^{2}} : \frac{x ^{2} - 5}{x ^{2}}

= \frac{x ^{2} - 5}{x ^{2}}

x \to 4 lim (lo g_{2} (x))

\int \frac{x ^{\frac{1}{2}} + 5}{3 x} d x

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

\int 1 + 100 x^{2} d x

\frac{1}{2} y^{^{'}} + 2 y = 0