derivative of-sin(xln(cos(x))+xcos(x))

Lösung

\frac{d}{d x} (- sin (x) ln (cos (x)) + x cos (x))

- cos (x) ln (cos (x)) + tan (x) sin (x) + cos (x) - x sin (x)

Schritte zur Lösung

\frac{d}{d x} (- sin (x) ln (cos (x)) + x cos (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

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

d er i v a t i v e y = e^{- 15 x}

\frac{d}{d x} (tan (x) sec (x))

d er i v a t i v e sin (x) + \frac{8}{7} cot (x)

s im pl i f y - 1

d er i v a t i v e y = x ∣ x ∣