derivative of xln(cos(x))

Lösung

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

ln (cos (x)) - x tan (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (cos (x))) = - tan (x)

= 1 \cdot ln (cos (x)) + (- tan (x)) x

Vereinfache

= ln (cos (x)) - x tan (x)