derivative of xsin(6/x)

Lösung

\frac{d}{d x} (x sin (\frac{6}{x}))

sin (\frac{6}{x}) - \frac{6 cos ( \frac{6}{x} )}{x}

Schritte zur Lösung

\frac{d}{d x} (x sin (\frac{6}{x}))

Wende die Produktregel an:

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

f = x, g = sin (\frac{6}{x})

= \frac{d x}{d x} sin (\frac{6}{x}) + \frac{d}{d x} (sin (\frac{6}{x})) x

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

\frac{d}{d x} (sin (\frac{6}{x})) = - \frac{6 cos ( \frac{6}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{6}{x}) + (- \frac{6 cos ( \frac{6}{x} )}{x ^{2}}) x

Vereinfache

1 \cdot sin (\frac{6}{x}) + (- \frac{6 cos ( \frac{6}{x} )}{x ^{2}}) x : sin (\frac{6}{x}) - \frac{6 cos ( \frac{6}{x} )}{x}

= sin (\frac{6}{x}) - \frac{6 cos ( \frac{6}{x} )}{x}

a re a y = \frac{x ^{2}}{2} - 3, y = - \frac{x ^{2}}{2} + 2 x

\int_{1}^{9} \frac{1}{x - 7} d x

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

\int \frac{x ^{2}}{x ^{2} - 4 x + 5} d x

\frac{d}{d x} (x + 5 e^{x})