derivative of 2x^{1/2}+x^{-1}-2

Lösung

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

\frac{x ^{2} - x ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{d}{d x} (2) = 0

= \frac{1}{x ^{\frac{1}{2}}} - \frac{1}{x ^{2}} - 0

Vereinfache

\frac{1}{x ^{\frac{1}{2}}} - \frac{1}{x ^{2}} - 0 : \frac{x ^{2} - x ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}

= \frac{x ^{2} - x ^{\frac{1}{2}}}{x ^{\frac{5}{2}}}

\int (4 sin (x) + \frac{2 x ^{5} - x}{x}) d x

d er i v a t i v e f (x) = \frac{4 x ^{\frac{3}{2}}}{x}

\frac{d}{d x} (cos (5 x - 9))

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

d er i v a t i v e y = 3 e^{4 x}