derivative of (ln(x)/(x^{6/5)})

Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{6}{5}}})

\frac{5 - 6 ln ( x )}{5 x ^{\frac{11}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{6}{5}}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{\frac{6}{5}} - \frac{d}{d x} ( x ^{\frac{6}{5}} ) ln ( x )}{( x ^{\frac{6}{5}} ) ^{2}}

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

\frac{d}{d x} (x^{\frac{6}{5}}) = \frac{6 x ^{\frac{1}{5}}}{5}

= \frac{\frac{1}{x} x ^{\frac{6}{5}} - \frac{6 x ^{\frac{1}{5}}}{5} ln ( x )}{( x ^{\frac{6}{5}} ) ^{2}}

Vereinfache

\frac{\frac{1}{x} x ^{\frac{6}{5}} - \frac{6 x ^{\frac{1}{5}}}{5} ln ( x )}{( x ^{\frac{6}{5}} ) ^{2}} : \frac{5 - 6 ln ( x )}{5 x ^{\frac{11}{5}}}

= \frac{5 - 6 ln ( x )}{5 x ^{\frac{11}{5}}}

d er i v a t i v e d ln (x) + a x^{n} + b e^{x}

\int_{0}^{7} 1 + x d x

d er i v a t i v e f (x) = 4 x sin (x)

\int cos^{2} (2 x) 2 d x

x \to 0 - lim (\frac{5}{x} - \frac{5}{x})