derivative xsqrt(ln(x))

Lösung

ableitung von

x ln (x)

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

Schritte zur Lösung

\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)

= \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}{2 x ln ( x )}

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

Vereinfache

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

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

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

d er i v a t i v e 6 e^{- 2 x} cos (4 x)

d er i v a t i v e f (x) = 5 x^{2} - 2 x - 7

y^{^{'}} = 0.04 y - 2000, y (0) = 25000

l a pl a ce t r an s f or m e^{3 (t - 2)}