derivative of (x^2-4x+3/(\sqrt[3]{x)})

Lösung

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

\frac{6 3 x x ^{\frac{5}{3}} - 12 3 x x ^{\frac{2}{3}} - x ^{2} + 4 x - 3}{3 x ^{\frac{4}{3}}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( 2 x - 4 ) 3 x - \frac{1}{3 x ^{\frac{2}{3}}} ( x ^{2} - 4 x + 3 )}{( 3 x ) ^{2}} : \frac{6 3 x x ^{\frac{5}{3}} - 12 3 x x ^{\frac{2}{3}} - x ^{2} + 4 x - 3}{3 x ^{\frac{4}{3}}}

= \frac{6 3 x x ^{\frac{5}{3}} - 12 3 x x ^{\frac{2}{3}} - x ^{2} + 4 x - 3}{3 x ^{\frac{4}{3}}}

\frac{\partial ^{2}}{\partial y ^{2}} (x y^{2} - 6 x^{2} - 3 y^{2})

\int_{0}^{1} e^{5 x} d x

y \to 2 lim (\frac{y ^{2} - 4}{y + 2})

d er i v a t i v e (2 x^{2} + 1)^{\frac{3}{2}}

im pl i c i t \frac{d y}{d x}, x^{2} = \frac{5 x + 4 y}{5 x - 4 y}