derivative of (ln(x)/(5x^3))

Lösung

\frac{d}{d x} (\frac{ln ( x )}{5 x ^{3}})

\frac{1 - 3 ln ( x )}{5 x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{5 x ^{3}})

Entferne die Konstante:

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

= \frac{1}{5} \frac{d}{d x} (\frac{ln ( x )}{x ^{3}})

Wende die Quotientenregel an:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( ln ( x ) ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ln ( x )}{( x ^{3} ) ^{2}}

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

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

= \frac{1}{5} \cdot \frac{\frac{1}{x} x ^{3} - 3 x ^{2} ln ( x )}{( x ^{3} ) ^{2}}

Vereinfache

\frac{1}{5} \cdot \frac{\frac{1}{x} x ^{3} - 3 x ^{2} ln ( x )}{( x ^{3} ) ^{2}} : \frac{1 - 3 ln ( x )}{5 x ^{4}}

= \frac{1 - 3 ln ( x )}{5 x ^{4}}

d er i v a t i v e 10000 - 9000 e^{- 0.3 t}

in v erse l a pl a ce \frac{s}{( s - 1 ) ^{2}}

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

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

im pl i c i t \frac{d y}{d x}, 4 x y = 8