derivative of (3x-4/((5x+2)^3))

Lösung

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

\frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((5 x + 2)^{3}) = 15 (5 x + 2)^{2}

= \frac{3 ( 5 x + 2 ) ^{3} - 15 ( 5 x + 2 ) ^{2} ( 3 x - 4 )}{( ( 5 x + 2 ) ^{3} ) ^{2}}

Vereinfache

\frac{3 ( 5 x + 2 ) ^{3} - 15 ( 5 x + 2 ) ^{2} ( 3 x - 4 )}{( ( 5 x + 2 ) ^{3} ) ^{2}} : \frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

= \frac{6 ( - 5 x + 11 )}{( 5 x + 2 ) ^{4}}

\int_{0}^{3} \frac{1}{36 - x ^{2}} d x

d er i v a t i v e f (x) = (6 x + 2)^{3}

\frac{d}{d x} (\frac{x ^{4}}{4} + \frac{8}{9} x^{3} - x^{2} + 3 x - 8)

x \to 0 lim (\frac{x ^{3}}{3})

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