derivative of (x-5/(3x-4))

Lösung

\frac{d}{d x} (\frac{x - 5}{3 x - 4})

\frac{11}{( 3 x - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 5}{3 x - 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( 3 x - 4 ) - \frac{d}{d x} ( 3 x - 4 ) ( x - 5 )}{( 3 x - 4 ) ^{2}}

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

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

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

Vereinfache

\frac{1 \cdot ( 3 x - 4 ) - 3 ( x - 5 )}{( 3 x - 4 ) ^{2}} : \frac{11}{( 3 x - 4 ) ^{2}}

= \frac{11}{( 3 x - 4 ) ^{2}}

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

\frac{d x}{d y} = - x^{2} + 7 x - 8

\int \frac{x ^{4} - 2 x ^{2} + 3}{x ^{2}} d x

n = 1 \sum \infty \frac{n ^{n}}{n !}

4 \frac{d y}{d x} + 28 y = 7