derivative of xln(x^9)

Lösung

\frac{d}{d x} (x ln (x^{9}))

9 ln (x) + 9

Schritte zur Lösung

\frac{d}{d x} (x ln (x^{9}))

Wende die Produktregel an:

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

f = x, g = ln (x^{9})

= \frac{d x}{d x} ln (x^{9}) + \frac{d}{d x} (ln (x^{9})) x

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

\frac{d}{d x} (ln (x^{9})) = \frac{9}{x}

= 1 \cdot ln (x^{9}) + \frac{9}{x} x

Vereinfache

1 \cdot ln (x^{9}) + \frac{9}{x} x : 9 ln (x) + 9

= 9 ln (x) + 9

\frac{d}{d x} ((1 + x^{2}) (x^{\frac{3}{4}} - x^{- 3}))

x \to 0 - lim (\frac{e ^{2 x}}{3 x})

\frac{\partial}{\partial x} (A (e^{- x} - e^{- x} x))

n = 0 \sum \infty 0.0 5^{n}

\int 2 r 4 - r^{2} d r