derivative of (x^3+7/x)

Lösung

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

\frac{2 x ^{3} - 7}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

= \frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 7 )}{x ^{2}}

Vereinfache

\frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 7 )}{x ^{2}} : \frac{2 x ^{3} - 7}{x ^{2}}

= \frac{2 x ^{3} - 7}{x ^{2}}

\int sin^{3} (5 x) cos^{3} (5 x) d x

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

\frac{d}{d x} (\frac{x + 2}{x ^{2}})

t a y l or tan (x), \frac{π}{4}

y^{^{'}} = \frac{2 - e ^{x}}{3 + 2 y}, y (0) = 0