derivative of xln(x^{15})

Lösung

\frac{d}{d x} (x ln (x^{15}))

15 ln (x) + 15

Schritte zur Lösung

\frac{d}{d x} (x ln (x^{15}))

Wende die Produktregel an:

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

f = x, g = ln (x^{15})

= \frac{d x}{d x} ln (x^{15}) + \frac{d}{d x} (ln (x^{15})) x

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

\frac{d}{d x} (ln (x^{15})) = \frac{15}{x}

= 1 \cdot ln (x^{15}) + \frac{15}{x} x

Vereinfache

1 \cdot ln (x^{15}) + \frac{15}{x} x : 15 ln (x) + 15

= 15 ln (x) + 15

d er i v a t i v e \frac{1}{27} (9 x^{2} + 6)^{\frac{3}{2}}

x \to \infty lim (\frac{x}{3})

\int \frac{1}{e ^{x} + 1} d x

n = 0 \sum \infty \frac{1}{( 2 n + 1 ) ^{3}}

n \to \infty lim (- 7^{n})