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_{1}^{3} 11 r^{3} ln (r) d r

y^{^{''}} + 25 y = 40 sin (5 t)

\frac{\partial}{\partial y} (x y + y)

l a pl a ce t r an s f or m 10 e^{(- 10 t)}

\int e^{4 x} x d x