derivative of xln^3(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

1 \cdot ln^{3} (x) + \frac{3 ln ^{2} ( x )}{x} x : ln^{3} (x) + 3 ln^{2} (x)

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

\int \frac{11 x ^{3}}{9 + x ^{2}} d x

\int \frac{1}{( x - 3 ) ( x - 2 )} d x

\frac{\partial}{\partial x} (2 x^{2} - 5 y^{2})

\int_{- 2}^{6} 4 x - x^{2} + 12 d x

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1