derivative of sin(xln(2x))

Lösung

\frac{d}{d x} (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} (x \cdot e^{- 3 x})

\int \frac{cos ( θ )}{1 + sin ^{2} ( θ )} d θ

\int (1 + y e^{x y}) d x

\int \frac{1}{x ( ln ( x ) ) ^{2}} d x

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 1})