derivative of (x^2+100/x)

Lösung

\frac{d}{d x} (\frac{x ^{2} + 100}{x})

\frac{x ^{2} - 100}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 100}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 100 ) x - \frac{d x}{d x} ( x ^{2} + 100 )}{x ^{2}}

\frac{d}{d x} (x^{2} + 100) = 2 x

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

= \frac{2 xx - 1 \cdot ( x ^{2} + 100 )}{x ^{2}}

Vereinfache

\frac{2 xx - 1 \cdot ( x ^{2} + 100 )}{x ^{2}} : \frac{x ^{2} - 100}{x ^{2}}

= \frac{x ^{2} - 100}{x ^{2}}

x \to 2 lim (ln (2))

\frac{d}{d x} (- \frac{1}{x ^{4}} - \frac{5}{x ^{2}})

a re a 4 x^{4} - 3 x^{2}, 6 x^{2}

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

d er i v a t i v e f (x) = x^{9} arccos (x)