derivative sin(x)ln(6x)

Lösung

ableitung von

sin (x) ln (6 x)

cos (x) ln (6 x) + \frac{sin ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (sin (x) ln (6 x))

Wende die Produktregel an:

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

f = sin (x), g = ln (6 x)

= \frac{d}{d x} (sin (x)) ln (6 x) + \frac{d}{d x} (ln (6 x)) sin (x)

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

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= cos (x) ln (6 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (6 x) + \frac{sin ( x )}{x}

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