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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

sec (\frac{1}{x}) tan (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

= sec (\frac{1}{x}) tan (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

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

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

Vereinfache

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

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

x \to 1 lim (- 1)

\int \frac{32 r ^{7} d r}{2 - r ^{8}} d x

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

\int_{1}^{3} \frac{x ^{2} + 7}{4 x - x ^{2}} d x

\frac{\partial}{\partial x} (2 x y e^{- x^{2} - y^{2}})