derivative of (x^2+9/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

n = 0 \sum \infty e^{- \frac{5 n}{2}}

\frac{\partial}{\partial x} (x^{3} e^{y} + cos (y))

\int_{1}^{e^{2}} x^{2} ln (x) d x

d er i v a t i v e \frac{x + 4}{x ^{3} + x - 5}