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

Lösung

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

\frac{- x ^{2} + 6 x - 8}{x ^{3} ∣ x - 2 ∣}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{\frac{x - 2}{∣ x - 2 ∣} x ^{2} - 2 x ∣ x - 2 ∣}{( x ^{2} ) ^{2}} : \frac{- x ^{2} + 6 x - 8}{x ^{3} ∣ x - 2 ∣}

= \frac{- x ^{2} + 6 x - 8}{x ^{3} ∣ x - 2 ∣}

\int_{- 3}^{5} 6 - y - \frac{( y - 3 ) ^{2}}{4} d y

d er i v a t i v e f (x) = 7 tan^{3} (x)

d er i v a t i v e 1 6^{x}

\int + \frac{16}{( 64 x ^{2} + 1 ) ^{2}} d x

\frac{d y}{d x} - cos (x) y = \frac{1}{100} cos (x)