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Beliebt Rechnen >

derivative of 1/2 ln(x/2)

Lösung

\frac{d}{d x} (\frac{1}{2} ln (\frac{x}{2}))

Lösung

\frac{1}{2 x}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2} ln (\frac{x}{2}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{2} \cdot \frac{1}{\frac{x}{2}} \cdot \frac{1}{2}

Vereinfache

\frac{1}{2} \cdot \frac{1}{\frac{x}{2}} \cdot \frac{1}{2} : \frac{1}{2 x}

= \frac{1}{2 x}

Graph

Beliebte Beispiele

derivative of x^{2/3}(x-4)

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

derivative of (2x-8^5)

\frac{d}{d x} ((2 x - 8)^{5})

laplacetransform f(t)=t^2e^{3t}

l a pl a ce t r an s f or m f (t) = t^{2} e^{3 t}

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

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

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

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