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

Lösung

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

1 - \frac{x}{2} + \frac{x ^{2}}{9}

Schritte zur Lösung

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

Vereinfache

x - (\frac{x}{2})^{2} + (\frac{x}{3})^{3} : x - \frac{x ^{2}}{4} + \frac{x ^{3}}{27}

= \frac{d}{d x} (x - \frac{x ^{2}}{4} + \frac{x ^{3}}{27})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} - \frac{d}{d x} (\frac{x ^{2}}{4}) + \frac{d}{d x} (\frac{x ^{3}}{27})

\frac{d x}{d x} = 1

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

\frac{d}{d x} (\frac{x ^{3}}{27}) = \frac{x ^{2}}{9}

= 1 - \frac{x}{2} + \frac{x ^{2}}{9}

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

d er i v a t i v e h (x) = ln (x + x^{2} - 7)

in v erse l a pl a ce \frac{- 2 s + 1}{s ^{2} + 2 s - 8}

x \to 0 lim (\frac{x + 4}{x})

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 9 y^{3})