derivative (2x^3-6)/(x^4)

Lösung

ableitung von

\frac{2 x ^{3} - 6}{x ^{4}}

\frac{2 ( - x ^{3} + 12 )}{x ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{3} - 6}{x ^{4}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{3} - 6 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 2 x ^{3} - 6 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (2 x^{3} - 6) = 6 x^{2}

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

= \frac{6 x ^{2} x ^{4} - 4 x ^{3} ( 2 x ^{3} - 6 )}{( x ^{4} ) ^{2}}

Vereinfache

\frac{6 x ^{2} x ^{4} - 4 x ^{3} ( 2 x ^{3} - 6 )}{( x ^{4} ) ^{2}} : \frac{2 ( - x ^{3} + 12 )}{x ^{5}}

= \frac{2 ( - x ^{3} + 12 )}{x ^{5}}

\frac{\partial}{\partial x} (30 x^{5} y^{4} - 20 x^{4} y^{3})

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

t an g e n t x^{2} + y^{2} = 169, (12, - 5)

\frac{d}{d x} ((4 x - 13) ln ((2 x - 7) (x - 3)))

\int_{- 2}^{3} (8 z^{3} + 3 z - 1) d z