derivative of (x^3+9/x)

Lösung

\frac{d}{d x} (\frac{x ^{3} + 9}{x})

\frac{2 x ^{3} - 9}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3} + 9}{x})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x^{3} + 9) = 3 x^{2}

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

= \frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 9 )}{x ^{2}}

Vereinfache

\frac{3 x ^{2} x - 1 \cdot ( x ^{3} + 9 )}{x ^{2}} : \frac{2 x ^{3} - 9}{x ^{2}}

= \frac{2 x ^{3} - 9}{x ^{2}}

y^{^{'}} = \frac{y ^{3} + 1}{( 3 x y ^{2} )}

\frac{\partial}{\partial x} (3 x y^{2})

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

d er i v a t i v e f (x) = 4 x + 32

a re a f (x) = ((25 - x^{2})^{\frac{1}{2}}), \frac{4}{3} x, 5