derivative of ((x^3/(x^4-2x))^3)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

\int x 5 - x d x

d er i v a t i v e f (x) = ln (4^{x} + 8^{x})

\frac{d y}{d x} + 3 x^{2} y = 9 x^{2}

d er i v a t i v e - \frac{1}{x ^{2} ( sec ^{2} ( y ) )}