derivative of sin(1/(sqrt(x)))

Lösung

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

- \frac{cos ( \frac{1}{x} )}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

cos (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

= cos (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

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

= cos (\frac{1}{x}) (- \frac{1}{2 x ^{\frac{3}{2}}})

Vereinfache

cos (\frac{1}{x}) (- \frac{1}{2 x ^{\frac{3}{2}}}) : - \frac{cos ( \frac{1}{x} )}{2 x ^{\frac{3}{2}}}

= - \frac{cos ( \frac{1}{x} )}{2 x ^{\frac{3}{2}}}

\int \frac{x e ^{x}}{2} d x

\frac{\partial}{\partial x} (ln (x + 3 y + 7 z))

\int tan^{3} (x) (sec (x))^{\frac{3}{2}} d x

\frac{\partial}{\partial y} (2 y^{2} + 3 x)

x \to 0 lim (\frac{3}{0})