derivative y=xln(x)cos(x)

Lösung

ableitung von

y = x ln (x) cos (x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

1 \cdot ln (x) cos (x) + (\frac{cos ( x )}{x} - sin (x) ln (x)) x : ln (x) cos (x) + cos (x) - x sin (x) ln (x)

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

\int \frac{3 x ^{3} + 5 x}{x ^{2} - x - 2} d x

x \to - \infty lim (arccos (x))

\int \frac{x ^{2} - 15 L}{x + 7} d x

d er i v a t i v e \frac{1 - 3 x - x ^{2}}{x ^{2} - 3}

l a pl a ce t r an s f or m 2 t^{3}