derivative of x^3ln|1+x|

Lösung

\frac{d}{d x} (x^{3} ln ∣ 1 + x ∣)

3 x^{2} ln ∣ 1 + x ∣ + \frac{x ^{3}}{1 + x}

Schritte zur Lösung

\frac{d}{d x} (x^{3} ln ∣ 1 + x ∣)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = ln ∣ 1 + x ∣

= \frac{d}{d x} (x^{3}) ln ∣ 1 + x ∣ + \frac{d}{d x} (ln ∣ 1 + x ∣) x^{3}

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

\frac{d}{d x} (ln ∣ 1 + x ∣) = \frac{1}{1 + x}

= 3 x^{2} ln ∣ 1 + x ∣ + \frac{1}{1 + x} x^{3}

\frac{1}{1 + x} x^{3} = \frac{x ^{3}}{1 + x}

= 3 x^{2} ln ∣ 1 + x ∣ + \frac{x ^{3}}{1 + x}

\int \frac{x ^{2} - 4 x + 9}{x ^{2} - 6 x + 9} d x

d er i v a t i v e arctan (9 x)

\int sin^{3} (3 x) cos^{3} (3 x) d x

x \to 0 lim (cot (3 x))

x \to - 1 lim (3 x + 4)