derivative (\sqrt[3]{x})/(x-9)

Lösung

ableitung von

\frac{3 x}{x - 9}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x}{x - 9})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x - 9) = 1

= \frac{\frac{1}{3 x ^{\frac{2}{3}}} ( x - 9 ) - 1 \cdot 3 x}{( x - 9 ) ^{2}}

Vereinfache

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

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

t an g e n t (x^{3} - 4 x)^{10}

\int \frac{1}{x ^{2} + 7 x + 12} d x

\int (sec (x) tan (x) - (sec (x))^{2}) d x

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

d er i v a t i v e f (x) = 3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}