derivative of (x^4/4 ln(x)-(x^4)/(16))

Lösung

\frac{d}{d x} (\frac{x ^{4}}{4} ln (x) - \frac{x ^{4}}{16})

x^{3} ln (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{4}}{4} ln (x) - \frac{x ^{4}}{16})

Vereinfache

\frac{x ^{4}}{4} ln (x) - \frac{x ^{4}}{16} : \frac{x ^{4} ln ( x )}{4} - \frac{x ^{4}}{16}

= \frac{d}{d x} (\frac{x ^{4} ln ( x )}{4} - \frac{x ^{4}}{16})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{4} ln ( x )}{4}) - \frac{d}{d x} (\frac{x ^{4}}{16})

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

\frac{d}{d x} (\frac{x ^{4}}{16}) = \frac{x ^{3}}{4}

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

Vereinfache

= x^{3} ln (x)

x \to - \infty lim (x + x^{3})

s l o p e in t erce pt (1.2) (4.4)

\int \frac{x ^{3}}{x ^{2} - 81} d x

d er i v a t i v e y (θ) = \frac{sin ( θ )}{5} + \frac{c}{θ}

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