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Beliebt Rechnen >

derivative of (x^5/5-1/2 x^{-2})

Lösung

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

Lösung

x^{4} + \frac{1}{x ^{3}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (\frac{x ^{5}}{5}) = x^{4}

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

= x^{4} - (- \frac{1}{x ^{3}})

Vereinfache

= x^{4} + \frac{1}{x ^{3}}

Graph

Beliebte Beispiele

derivative 4/(x^2+4)

d er i v a t i v e \frac{4}{x ^{2} + 4}

integral of 9sin^3(xco)s^2x

\int 9 sin^{3} (x co) s^{2} x d x

derivative (2u^2)/((u^2+u)^3)

d er i v a t i v e \frac{2 u ^{2}}{( u ^{2} + u ) ^{3}}

integral of 1/((3x)^2)

\int \frac{1}{( 3 x ) ^{2}} d x

integral from 0 to 6 of pi(3)^2

\int_{0}^{6} π (3)^{2} d x