derivative of ln((3e^x/(2x^2)))

Lösung

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

\frac{x - 2}{x}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{\frac{3 e ^{x}}{2 x ^{2}}} \cdot \frac{3 e ^{x} ( x - 2 )}{2 x ^{3}} : \frac{x - 2}{x}

= \frac{x - 2}{x}

t a y l or x, 100

\frac{d y}{d x} = x + 2 y, y (0) = 7

\frac{d}{d x} (e^{x} \cdot cos (y))

\int y e^{y} d y

x \to 0 lim (\frac{x ^{2} + 1}{x})