derivative ((x^4+2))/(ln(x))

Lösung

ableitung von

\frac{( x ^{4} + 2 )}{ln ( x )}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x^{4} + 2) = 4 x^{3}

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

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

Vereinfache

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

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

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

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