(\partial)/(\partial x)(ln(x/(20)))

Lösung

\frac{\partial}{\partial x} (ln (\frac{x}{20}))

\frac{1}{x}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (\frac{x}{20}))

Wende die Kettenregel an:

\frac{1}{\frac{x}{20}} \frac{\partial}{\partial x} (\frac{x}{20})

= \frac{1}{\frac{x}{20}} \frac{\partial}{\partial x} (\frac{x}{20})

\frac{\partial}{\partial x} (\frac{x}{20}) = \frac{1}{20}

= \frac{1}{\frac{x}{20}} \cdot \frac{1}{20}

Vereinfache

\frac{1}{\frac{x}{20}} \cdot \frac{1}{20} : \frac{1}{x}

= \frac{1}{x}

x \to 0 lim (x \cdot \frac{1}{x})

\int \frac{x}{( 1 + x ) ^{4}} d x

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

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

d er i v a t i v e f (x) = ln (x^{3} - 1)