derivative of (x-sqrt(x)+6x^4^3)

Lösung

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

2592 x^{11} + 972 x^{8} - 864 x^{7} x + 108 x^{5} - 180 x^{4} x + 90 x^{4} + 3 x^{2} - 6 x x + 6 x - 54 x^{\frac{15}{2}} - 18 x^{\frac{9}{2}} + \frac{3 ( - x ^{\frac{3}{2}} - x )}{2}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x - x + 6 x^{4}) = 1 - \frac{1}{2 x} + 24 x^{3}

= 3 (x - x + 6 x^{4})^{2} (1 - \frac{1}{2 x} + 24 x^{3})

Vereinfache

3 (x - x + 6 x^{4})^{2} (1 - \frac{1}{2 x} + 24 x^{3}) : 2592 x^{11} + 972 x^{8} - 864 x^{7} x + 108 x^{5} - 180 x^{4} x + 90 x^{4} + 3 x^{2} - 6 x x + 6 x - 54 x^{\frac{15}{2}} - 18 x^{\frac{9}{2}} + \frac{3 ( - x ^{\frac{3}{2}} - x )}{2}

= 2592 x^{11} + 972 x^{8} - 864 x^{7} x + 108 x^{5} - 180 x^{4} x + 90 x^{4} + 3 x^{2} - 6 x x + 6 x - 54 x^{\frac{15}{2}} - 18 x^{\frac{9}{2}} + \frac{3 ( - x ^{\frac{3}{2}} - x )}{2}

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

l a pl a ce t r an s f or m (t + 6)^{3}

h \to 0 lim (- \frac{5 h}{x ( x + h )})

d er i v a t i v e \frac{x ^{3}}{7}

\int 3 x x + 2 d x