derivative of (7x-4/(-3x+3))

Lösung

\frac{d}{d x} (\frac{7 x - 4}{- 3 x + 3})

\frac{1}{( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x - 4}{- 3 x + 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 7 x - 4 ) ( - 3 x + 3 ) - \frac{d}{d x} ( - 3 x + 3 ) ( 7 x - 4 )}{( - 3 x + 3 ) ^{2}}

\frac{d}{d x} (7 x - 4) = 7

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

= \frac{7 ( - 3 x + 3 ) - ( - 3 ) ( 7 x - 4 )}{( - 3 x + 3 ) ^{2}}

Vereinfache

\frac{7 ( - 3 x + 3 ) - ( - 3 ) ( 7 x - 4 )}{( - 3 x + 3 ) ^{2}} : \frac{1}{( x - 1 ) ^{2}}

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

d er i v a t i v e - 6

x \to 5 lim (2 x - 5)

\frac{d y}{d t} = (1 + t) (1 + y)

t \to 1 + lim (\frac{∣ 1 - t ∣}{1 - t})

\frac{d}{d x} (e^{x^{2} - y^{2}})