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

Lösung

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

\frac{8 x ^{2} - 56 x - 21}{( 2 x - 7 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (2 x - 7) = 2

= \frac{( 8 x + 3 ) ( 2 x - 7 ) - 2 ( 4 x ^{2} + 3 x )}{( 2 x - 7 ) ^{2}}

Multipliziere aus

(8 x + 3) (2 x - 7) - 2 (4 x^{2} + 3 x) : 8 x^{2} - 56 x - 21

= \frac{8 x ^{2} - 56 x - 21}{( 2 x - 7 ) ^{2}}

d er i v a t i v e 2^{70}

y^{^{'''}} + 3 y^{^{''}} + 2 y^{^{'}} = 0

x \to 0 lim (\frac{8 ^{x} - 1}{x})

\frac{d}{d x} (x^{3} - 3 x^{2} + 3 x - 1)

\int 6 cos (x) d x