derivative of ln(sqrt((3x^4+2/(4x))))

Lösung

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

\frac{9 x ^{4} - 2}{2 x ( 3 x ^{4} + 2 )}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Kettenregel an:

\frac{1}{\frac{3 x ^{4} + 2}{2 x}} \frac{d}{d x} (\frac{3 x ^{4} + 2}{2 x})

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

\frac{d}{d x} (\frac{3 x ^{4} + 2}{2 x}) = \frac{9 x ^{4} - 2}{4 x x 3 x ^{4} + 2}

= \frac{1}{\frac{3 x ^{4} + 2}{2 x}} \cdot \frac{9 x ^{4} - 2}{4 x x 3 x ^{4} + 2}

Vereinfache

\frac{1}{\frac{3 x ^{4} + 2}{2 x}} \cdot \frac{9 x ^{4} - 2}{4 x x 3 x ^{4} + 2} : \frac{9 x ^{4} - 2}{2 x ( 3 x ^{4} + 2 )}

= \frac{9 x ^{4} - 2}{2 x ( 3 x ^{4} + 2 )}

d er i v a t i v e 6^{4 - x^{2}}

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

\frac{d y}{d x} = 4 e^{3 x - 4 y}

\frac{d}{d x} (\frac{6}{2 ^{x}})

\frac{d}{d x} (\frac{x}{x + 5})