derivative ln(x)sqrt(x)

Lösung

ableitung von

ln (x) x

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

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

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

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

Vereinfache

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

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

t an g e n t f (x) = x^{4} + 4 e^{x}, (0, 4)

\frac{d y}{d t} = - 2 (y - 4)

\int \frac{x ^{2} + 16}{x ^{4}} d x

x \to 1 lim (x^{2} + 3 x - 4)

d er i v a t i v e \frac{( x ^{2} e ^{x} )}{x ^{2} + e ^{x}}