derivative of (3x-9/(x+5))

Lösung

\frac{d}{d x} (\frac{3 x - 9}{x + 5})

\frac{24}{( x + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 9}{x + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x - 9 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( 3 x - 9 )}{( x + 5 ) ^{2}}

\frac{d}{d x} (3 x - 9) = 3

\frac{d}{d x} (x + 5) = 1

= \frac{3 ( x + 5 ) - 1 \cdot ( 3 x - 9 )}{( x + 5 ) ^{2}}

Vereinfache

\frac{3 ( x + 5 ) - 1 \cdot ( 3 x - 9 )}{( x + 5 ) ^{2}} : \frac{24}{( x + 5 ) ^{2}}

= \frac{24}{( x + 5 ) ^{2}}

\int (π - x) \cdot cos (n x) d x

\int \frac{x ^{2}}{( x ^{3} - 5 ) ^{2}} d x

\frac{d y}{d x} = - \frac{1}{x}

y^{^{'}} + y = e^{2 t}, y (0) = - 1

\int (1 - ln (x)) d x