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Beliebt Rechnen >

derivative f(x)=(x^3)/6+1/(2x)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Graph

Beliebte Beispiele

derivative of (1+cos(x)/(sin(x)))

\frac{d}{d x} (\frac{1 + cos ( x )}{sin ( x )})

(\partial)/(\partial x)(3x-sqrt(3y^2+z^2))

\frac{\partial}{\partial x} (3 x - 3 y^{2} + z^{2})

integral of (x-e^{-x})^2

\int (x - e^{- x})^{2} d x

tangent f(x)=(x^2)/(x-7)

t an g e n t f (x) = \frac{x ^{2}}{x - 7}

derivative of 5x-6

\frac{d}{d x} (5 x - 6)