derivative of (x^2+4/x)

Lösung

\frac{d}{d x} (\frac{x ^{2} + 4}{x})

\frac{x ^{2} - 4}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 4}{x})

Wende die Quotientenregel an:

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

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

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

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

= \frac{2 xx - 1 \cdot ( x ^{2} + 4 )}{x ^{2}}

Vereinfache

\frac{2 xx - 1 \cdot ( x ^{2} + 4 )}{x ^{2}} : \frac{x ^{2} - 4}{x ^{2}}

= \frac{x ^{2} - 4}{x ^{2}}

in v erse l a pl a ce \frac{1}{2 s + 3}

\frac{\partial}{\partial x} (x \cdot e^{x + 2 y})

x \to \infty lim (\frac{sin ( 13 x )}{3 x})

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

d er i v a t i v e f (x) = x^{3} - 27 x + 9