derivative (2x-4)/(x^{1/2)}

Lösung

ableitung von

\frac{2 x - 4}{x ^{\frac{1}{2}}}

\frac{x + 2}{x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x - 4}{x ^{\frac{1}{2}}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x - 4 ) x ^{\frac{1}{2}} - \frac{d}{d x} ( x ^{\frac{1}{2}} ) ( 2 x - 4 )}{( x ^{\frac{1}{2}} ) ^{2}}

\frac{d}{d x} (2 x - 4) = 2

\frac{d}{d x} (x^{\frac{1}{2}}) = \frac{1}{2 x ^{\frac{1}{2}}}

= \frac{2 x ^{\frac{1}{2}} - \frac{1}{2 x ^{\frac{1}{2}}} ( 2 x - 4 )}{( x ^{\frac{1}{2}} ) ^{2}}

Vereinfache

\frac{2 x ^{\frac{1}{2}} - \frac{1}{2 x ^{\frac{1}{2}}} ( 2 x - 4 )}{( x ^{\frac{1}{2}} ) ^{2}} : \frac{x + 2}{x ^{\frac{3}{2}}}

= \frac{x + 2}{x ^{\frac{3}{2}}}

d er i v a t i v e sin^{5} (x) + 4

d er i v a t i v e y = x^{4} - 3 x^{- 2} + 1

d er i v a t i v e 1 7^{x - 1}

\frac{d}{d b} (1 b)

s im pl i f y (x^{3})^{\frac{1}{2}}