derivative of x/(|x|)

Lösung

\frac{d}{d x} (\frac{x}{∣ x ∣})

0

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{∣ x ∣})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (∣ x ∣) = \frac{x}{∣ x ∣}

= \frac{1 \cdot ∣ x ∣ - \frac{x}{∣ x ∣} x}{∣ x ∣ ^{2}}

Vereinfache

\frac{1 \cdot ∣ x ∣ - \frac{x}{∣ x ∣} x}{∣ x ∣ ^{2}} : 0

= 0

\frac{\partial}{\partial x} (π)

- x \frac{d y}{d x} + y = 0

\int 24 x^{2} + 16 x d x

\frac{d}{d x} (\frac{z}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

in v erse l a pl a ce \frac{1}{( s + 1 ) ( s + 2 ) ^{2}}