derivative of (x^3+6/x)

Lösung

\frac{d}{d x} (\frac{x ^{3} + 6}{x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} + 6}{x})

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

= \frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 6 )}{x ^{2}}

Vereinfache

\frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 6 )}{x ^{2}} : \frac{2 x ^{3} - 6}{x ^{2}}

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

\frac{d}{d x} (\frac{8 + x}{1 - 8 x})

\int 19 sin^{3} (x co) s^{2} x d x

t an g e n t y = x^{2} + x, (- 1, 0)

\frac{d}{d x} (\frac{x ^{2}}{( x ^{2} - 1 ) ^{4}})

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