derivative of (ln(x)/(x^4))

Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{4}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{4}})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{\frac{1}{x} x ^{4} - 4 x ^{3} ln ( x )}{( x ^{4} ) ^{2}}

Vereinfache

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

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

\frac{d y}{d x} + y = e^{5 x}

3 y^{^{'}} - 9 x^{2} = 0

\frac{\partial}{\partial y} (e^{- 2 x} \cdot cos (2 y))

d er i v a t i v e f (x) = \frac{1 - 2 x}{5 + x}

\int \frac{4 x ^{3} - 8 x ^{2} + 5}{x ^{2} - 2 x} d x