derivative of sin(3/x)

Lösung

\frac{d}{d x} (sin (\frac{3}{x}))

- \frac{3 cos ( \frac{3}{x} )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (sin (\frac{3}{x}))

Wende die Kettenregel an:

cos (\frac{3}{x}) \frac{d}{d x} (\frac{3}{x})

= cos (\frac{3}{x}) \frac{d}{d x} (\frac{3}{x})

\frac{d}{d x} (\frac{3}{x}) = - \frac{3}{x ^{2}}

= cos (\frac{3}{x}) (- \frac{3}{x ^{2}})

Vereinfache

cos (\frac{3}{x}) (- \frac{3}{x ^{2}}) : - \frac{3 cos ( \frac{3}{x} )}{x ^{2}}

= - \frac{3 cos ( \frac{3}{x} )}{x ^{2}}

x \to 2 lim (\frac{x}{x + 2})

\frac{d}{d x} ((x^{2} + 1)^{3})

x \to - \infty lim (\frac{4 e ^{\frac{1}{x}} - 1}{1 + e ^{x}})

\frac{d}{d x} (5 x^{2} + 1)

d er i v a t i v e y = cos (x) sin (x)