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

Lösung

ableitung von

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

\frac{6 ( x ^{4} + 6 )}{x ^{4}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{6 ( x ^{4} + 6 )}{x ^{4}}

d er i v a t i v e (5 x^{2} + 8)^{8}

a re a x - 1, 2, 5

x \to 6 lim (\frac{24}{x} + x^{2})

x^{2} \cdot \frac{d y}{d x} + x (x + 2) y = e^{x}

\int x^{2} - e^{- x} d x