derivative of x^3*ln(x)

Lösung

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

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

Schritte zur Lösung

\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)

= \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}

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

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

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

d er i v a t i v e y = y

roo t s \frac{k x}{a ^{2} + x ^{2}}

t an g e n t f (x) = x (x - 2), at x = 1

\int_{0}^{2} x^{3} e^{x} d x

x \to 4 - lim (\frac{x - 9}{x - 4})