derivative of 9sqrt(x)-1/x

Lösung

\frac{d}{d x} (9 x - \frac{1}{x})

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

Schritte zur Lösung

\frac{d}{d x} (9 x - \frac{1}{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (9 x) - \frac{d}{d x} (\frac{1}{x})

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

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

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

Vereinfache

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

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

l a pl a ce t r an s f or m e^{20 t}

y^{^{''}} - 16 y^{^{'}} + 64 y = 0, y (0) = 1, y (1) = 0

x \to 0 lim ((1 - 2 x)^{\frac{3}{x}})

d er i v a t i v e ln (361 sin^{2} (x))

(x + y) d x + x d y = 0