derivative of (2x+3/(x+4))

Lösung

\frac{d}{d x} (\frac{2 x + 3}{x + 4})

\frac{5}{( x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x + 3}{x + 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x + 3 ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) ( 2 x + 3 )}{( x + 4 ) ^{2}}

\frac{d}{d x} (2 x + 3) = 2

\frac{d}{d x} (x + 4) = 1

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

Vereinfache

\frac{2 ( x + 4 ) - 1 \cdot ( 2 x + 3 )}{( x + 4 ) ^{2}} : \frac{5}{( x + 4 ) ^{2}}

= \frac{5}{( x + 4 ) ^{2}}

x \to 4 lim (\frac{x - 4}{x - 4})

d er i v a t i v e y = 5 x + 6

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{3})

\frac{d}{d x} (\frac{∣ x - 1 ∣}{∣ x - 3 ∣})

t a y l or x ln (x)