derivative of (sqrt(x)/(x+4))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{1 + e ^{2 x}}{e ^{x - 1}} d x

\int \frac{3}{x + 3 + x} d x

\int x + \frac{1}{x} - 7 d x

x \to 7 lim (5 x^{2} - 5 x + 6)

x \to 0 lim (\frac{1}{1 + cos ( x )})