derivative of (2x-1/(x+2))

Lösung

\frac{d}{d x} (\frac{2 x - 1}{x + 2})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x - 1}{x + 2})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int (\frac{3 x + x ^{5}}{x}) d x

y^{^{'}} = e^{8 x} - 6 x

d er i v a t i v e f (x) = \frac{40 t}{t + 2}

h \to 0 lim ((2 x + h) - 2 x)

d er i v a t i v e cos (\frac{1 - e ^{4 x}}{1 + e ^{4 x}})