derivative of \sqrt[3]{6x^2-x^3}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{3 ( 6 x ^{2} - x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x^{2} - x^{3})

= \frac{1}{3 ( 6 x ^{2} - x ^{3} ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x^{2} - x^{3})

\frac{d}{d x} (6 x^{2} - x^{3}) = 12 x - 3 x^{2}

= \frac{1}{3 ( 6 x ^{2} - x ^{3} ) ^{\frac{2}{3}}} (12 x - 3 x^{2})

Vereinfache

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

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

\int (x^{2} - 5) d x

y^{^{''}} + 10 y = 0

\int \frac{17 x ^{7}}{315} d x

d er i v a t i v e \frac{2 x ^{2} + 8 x + 8}{x}

\frac{\partial}{\partial x} ((x y)^{(\frac{1}{2})})