derivative of (ln(x)^2(sin(x)))

Lösung

\frac{d}{d x} ((ln (x))^{2} (sin (x)))

\frac{2 ln ( x ) sin ( x )}{x} + ln^{2} (x) cos (x)

Schritte zur Lösung

\frac{d}{d x} ((ln (x))^{2} (sin (x)))

Wende die Produktregel an:

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

f = (ln (x))^{2}, g = sin (x)

= \frac{d}{d x} ((ln (x))^{2}) sin (x) + \frac{d}{d x} (sin (x)) (ln (x))^{2}

\frac{d}{d x} ((ln (x))^{2}) = \frac{2 ln ( x )}{x}

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

= \frac{2 ln ( x )}{x} sin (x) + cos (x) (ln (x))^{2}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ln ( x ) sin ( x )}{x} + ln^{2} (x) cos (x)

(x^{2} + 2 x y - 4 y^{2}) d x - (x^{2} - 8 x y - 4 y^{2}) d y = 0

d er i v a t i v e sin (x) cos (x) - sin^{2} (x) + x

x \to 0 lim (\frac{e ^{8 x} - 1}{x})

s l o p e in t erce pt (2, 1), (- 4, - 2)

\int 7 x (x^{2} + 2)^{2} d x