derivative of sqrt(x)ln(4x)

Lösung

\frac{d}{d x} (x ln (4 x))

\frac{ln ( 4 x )}{2 x} + \frac{1}{x}

Schritte zur Lösung

\frac{d}{d x} (x ln (4 x))

Wende die Produktregel an:

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

f = x, g = ln (4 x)

= \frac{d}{d x} (x) ln (4 x) + \frac{d}{d x} (ln (4 x)) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

= \frac{1}{2 x} ln (4 x) + \frac{1}{x} x

Vereinfache

\frac{1}{2 x} ln (4 x) + \frac{1}{x} x : \frac{ln ( 4 x )}{2 x} + \frac{1}{x}

= \frac{ln ( 4 x )}{2 x} + \frac{1}{x}

a re a 4 - x, 0, - 2, 6

a re a y = 1, x = y^{\frac{5}{2}}, [0, 1]

\int 6 e^{- 6 x} d x

x \to 1 lim (ln (x) - ln (x - 1))

x \to 0 lim (\frac{x}{x ^{2} + y ^{2}})