derivative ((x^3)/(x^8+7))^2

Lösung

ableitung von

(\frac{x ^{3}}{x ^{8} + 7})^{2}

\frac{2 x ^{3} ( - 5 x ^{10} + 21 x ^{2} )}{( x ^{8} + 7 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{3}}{x ^{8} + 7})^{2})

Wende die Kettenregel an:

2 \cdot \frac{x ^{3}}{x ^{8} + 7} \frac{d}{d x} (\frac{x ^{3}}{x ^{8} + 7})

= 2 \cdot \frac{x ^{3}}{x ^{8} + 7} \frac{d}{d x} (\frac{x ^{3}}{x ^{8} + 7})

\frac{d}{d x} (\frac{x ^{3}}{x ^{8} + 7}) = \frac{- 5 x ^{10} + 21 x ^{2}}{( x ^{8} + 7 ) ^{2}}

= 2 \cdot \frac{x ^{3}}{x ^{8} + 7} \cdot \frac{- 5 x ^{10} + 21 x ^{2}}{( x ^{8} + 7 ) ^{2}}

Vereinfache

2 \cdot \frac{x ^{3}}{x ^{8} + 7} \cdot \frac{- 5 x ^{10} + 21 x ^{2}}{( x ^{8} + 7 ) ^{2}} : \frac{2 x ^{3} ( - 5 x ^{10} + 21 x ^{2} )}{( x ^{8} + 7 ) ^{3}}

= \frac{2 x ^{3} ( - 5 x ^{10} + 21 x ^{2} )}{( x ^{8} + 7 ) ^{3}}

h \to 0 lim (h^{4} cos (\frac{3}{h}))

\frac{\partial}{\partial x} (8 e^{x^{8} y})

\int \frac{sec ^{3} ( x )}{tan ^{4} ( x )} d x

\frac{d}{d y} (x^{2} + y^{2})

\frac{d}{d x} (\frac{x}{x + 10})