derivative ln(x)*x

Lösung

ableitung von

ln (x) \cdot x

1 + ln (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = ln (x), g = x

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

Vereinfache

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

= 1 + ln (x)

\frac{\partial}{\partial u} (4 sin (u) cos (v))

\frac{d}{d x} (5 x^{4} - \frac{4}{x})

x \to 0 + lim (tan (2 x))

t an g e n t (8 x + 9)^{- 2}

\frac{d}{d x} (x^{3} - 12 x)