derivative of 4x^3ln(x)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x^{3}, g = ln (x)

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

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

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

= 4 (3 x^{2} ln (x) + \frac{1}{x} x^{3})

\frac{1}{x} x^{3} = x^{2}

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

x \to - \infty lim (\frac{2 x ^{2} + 3}{2 x + 3})

x \to - 1 lim (3)

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

\int \frac{ln ( - 2 x )}{5 x} d x

a re a y = x^{2} - 7, y = 6 x