derivative of \sqrt[5]{(x^3-2/(x^3+2)})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{3} - 2}{x ^{3} + 2}) = \frac{12 x ^{2}}{( x ^{3} + 2 ) ^{2}}

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

Vereinfache

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

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

y^{^{'}} = x e^{6}

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

d er i v a t i v e (1 + 9 x^{2}) (x + x^{2})

\int \frac{2}{4 - 9 x ^{2}} d x

x \to - 4 lim (6 - 3 x)