derivative of x^4ln(x-1/3 x^3)

Lösung

\frac{d}{d x} (x^{4} ln (x) - \frac{1}{3} x^{3})

4 x^{3} ln (x) + x^{3} - x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{4} ln (x) - \frac{1}{3} x^{3})

Vereinfache

x^{4} ln (x) - \frac{1}{3} x^{3} : x^{4} ln (x) - \frac{x ^{3}}{3}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

a re a x^{2} - x, x

d er i v a t i v e G (t) = 5 t + \frac{7}{t}

d er i v a t i v e f (x) = \frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

\int_{- 1}^{1} π (x^{2} + 1)^{2} d x

\int 7 θ cos (θ) d θ