derivative f(x)= 2/(3x)-1/(6sqrt(x))

Lösung

ableitung von

f (x) = \frac{2}{3 x} - \frac{1}{6 x}

\frac{- 8 x ^{\frac{3}{2}} + x ^{2}}{12 x ^{\frac{7}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{3 x} - \frac{1}{6 x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{2}{3 x}) - \frac{d}{d x} (\frac{1}{6 x})

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

\frac{d}{d x} (\frac{1}{6 x}) = - \frac{1}{12 x ^{\frac{3}{2}}}

= - \frac{2}{3 x ^{2}} - (- \frac{1}{12 x ^{\frac{3}{2}}})

Vereinfache

- \frac{2}{3 x ^{2}} - (- \frac{1}{12 x ^{\frac{3}{2}}}) : \frac{- 8 x ^{\frac{3}{2}} + x ^{2}}{12 x ^{\frac{7}{2}}}

= \frac{- 8 x ^{\frac{3}{2}} + x ^{2}}{12 x ^{\frac{7}{2}}}

t a y l or sin (x), π

\frac{d P}{d t} = P (850 - P)

\frac{d y}{d x} = - y

y^{^{'}} + \frac{5}{x} y = 0

\int_{- \infty}^{0} x e^{x} d x