derivative y=sin(x)ln(2x)

Lösung

ableitung von

y = sin (x) ln (2 x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = sin (x), g = ln (2 x)

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

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= cos (x) ln (2 x) + \frac{1}{x} sin (x)

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

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

\frac{d}{d x} (\frac{6 arctan ( 2 x )}{5 e ^{3 x}})

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

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

d er i v a t i v e f (x) = a x^{4} + (a - 9) x^{2} - 9

n = 1 \sum \infty \frac{3 n}{n ^{2} + 4}