derivative of 2xln(x)

Lösung

\frac{d}{d x} (2 x ln (x))

2 (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (2 x ln (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x, g = ln (x)

= 2 (\frac{d x}{d x} ln (x) + \frac{d}{d x} (ln (x)) x)

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

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

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

Vereinfache

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

= 2 (ln (x) + 1)

\int \frac{1}{1 + 4 x - 1} d x

t an g e n t y = \frac{5 x}{1 + x ^{2}}, (5, \frac{25}{26})

\int w csc (4 w^{2} - 1) d w

\frac{d}{d x} (1.5 x - 0.25 x^{2})

l a pl a ce t r an s f or m cos (x)