derivative 3sin(x)ln(x)

Lösung

ableitung von

3 sin (x) ln (x)

3 (cos (x) ln (x) + \frac{sin ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (3 sin (x) ln (x))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (sin (x) ln (x))

Wende die Produktregel an:

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

f = sin (x), g = ln (x)

= 3 (\frac{d}{d x} (sin (x)) ln (x) + \frac{d}{d x} (ln (x)) sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

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

= 3 (cos (x) ln (x) + \frac{1}{x} sin (x))

\frac{1}{x} sin (x) = \frac{sin ( x )}{x}

= 3 (cos (x) ln (x) + \frac{sin ( x )}{x})

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

d er i v a t i v e y = \frac{1}{3} - 6

roo t s co sin (o)

d er i v a t i v e (s^{5} - 9)^{2}

\frac{d}{d x} (arctan (9 x))