derivative of (x^2+3/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y = x^{2} sin^{6} (x) + x cos^{- 2} (x)

x \to 4 lim ((3 x - 9)^{4})

d er i v a t i v e y = x + 7

\frac{d y}{d x} = (1 + 4 y^{2}) (1 + 3 x^{2})

x \to 0 lim (\frac{sin ( 7 x )}{sin ( 9 x )})