derivative of sqrt((3x+2/(5-4x)))

Lösung

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

\frac{23}{2 3 x + 2 ( - 4 x + 5 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

Wende die Kettenregel an:

\frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

= \frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x}) = \frac{23}{( 5 - 4 x ) ^{2}}

= \frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \cdot \frac{23}{( 5 - 4 x ) ^{2}}

Vereinfache

\frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \cdot \frac{23}{( 5 - 4 x ) ^{2}} : \frac{23}{2 3 x + 2 ( - 4 x + 5 ) ^{\frac{3}{2}}}

= \frac{23}{2 3 x + 2 ( - 4 x + 5 ) ^{\frac{3}{2}}}

\frac{\partial}{\partial x} (\frac{1}{ln ( \frac{y}{x} )})

s im pl i f y ln (\frac{( x + 6 ) ^{4} e ^{5 x^{3} - 3}}{x + 2 x ^{3}})

d er i v a t i v e ln (y^{2})

s im pl i f y \frac{7}{4} x^{4} - \frac{6}{5} x^{3}

x \to 0 lim (\frac{e ^{x} - 1}{17 x})