derivative of 1/2 x^3+3/(2x)

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{1}{2} x^{3} + \frac{3}{2 x} : \frac{x ^{3}}{2} + \frac{3}{2 x}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

d er i v a t i v e y = \frac{5}{2 x ^{3}}

\frac{\partial}{\partial x} (e^{- (\frac{x ^{2} + y ^{2}}{2})})

\int_{2}^{6} \frac{x}{x ^{2} + 6 x + 13} d x