derivative of 1/8 x^4+1/4 x^{-2}

Lösung

\frac{d}{d x} (\frac{1}{8} x^{4} + \frac{1}{4} x^{- 2})

\frac{x ^{3}}{2} - \frac{1}{2 x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{8} x^{4} + \frac{1}{4} x^{- 2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{8} x^{4}) + \frac{d}{d x} (\frac{1}{4} x^{- 2})

\frac{d}{d x} (\frac{1}{8} x^{4}) = \frac{x ^{3}}{2}

\frac{d}{d x} (\frac{1}{4} x^{- 2}) = - \frac{1}{2 x ^{3}}

= \frac{x ^{3}}{2} - \frac{1}{2 x ^{3}}

\int_{0}^{\infty} E (t) d t

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

\int (e^{x^{3}}) d x

\frac{d}{d x} (sin^{2} (3 x) + cos (5 x^{2}))

\int_{0}^{\infty} e^{- 2 t} d t