derivative of (3-8x/(x+4))

Lösung

\frac{d}{d x} (\frac{3 - 8 x}{x + 4})

- \frac{35}{( x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 - 8 x}{x + 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 - 8 x ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) ( 3 - 8 x )}{( x + 4 ) ^{2}}

\frac{d}{d x} (3 - 8 x) = - 8

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

= \frac{( - 8 ) ( x + 4 ) - 1 \cdot ( 3 - 8 x )}{( x + 4 ) ^{2}}

Vereinfache

\frac{( - 8 ) ( x + 4 ) - 1 \cdot ( 3 - 8 x )}{( x + 4 ) ^{2}} : - \frac{35}{( x + 4 ) ^{2}}

= - \frac{35}{( x + 4 ) ^{2}}

in v erse l a pl a ce \frac{s ^{3} + s + 6}{s ^{4} ( s + 2 )}

\int_{7}^{8} \frac{x}{x ^{2} - 3} d x

x \to 7 + lim (3 x + 5)

d er i v a t i v e x

\frac{d y}{d t} = 2 y - 3 e^{- t}