derivative f(x)=(ln(x^2))/x

Lösung

ableitung von

f (x) = \frac{ln ( x ^{2} )}{x}

\frac{2 - ln ( x ^{2} )}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

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

d er i v a t i v e f (x) = e^{- 5 x} cos (3 x)

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

\int_{- 1}^{2} (x + 2) - (x^{2}) d x

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

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