derivative of (3x-7/(2x+4))

Lösung

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

\frac{13}{2 ( x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 x - 7) = 3

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

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

Vereinfache

\frac{3 ( 2 x + 4 ) - 2 ( 3 x - 7 )}{( 2 x + 4 ) ^{2}} : \frac{13}{2 ( x + 2 ) ^{2}}

= \frac{13}{2 ( x + 2 ) ^{2}}

d er i v a t i v e f (x) = \frac{7 + tan ( x )}{5 - tan ( x )}

\frac{\partial}{\partial x} (- 3 y cos (3 x))

(x y^{2} - 3 y) d x + (x^{2} y - 3 x) d y = 0

\int \frac{1 - x}{3 e ^{x}} d x

x \to 3 lim (x^{2} - 4)