derivative 1/(cot(1/t))

Lösung

ableitung von

\frac{1}{cot ( \frac{1}{t} )}

- \frac{sec ^{2} ( \frac{1}{t} )}{t ^{2}}

Schritte zur Lösung

\frac{d}{d t} (\frac{1}{cot ( \frac{1}{t} )})

Vereinfache

\frac{1}{cot ( \frac{1}{t} )} : tan (\frac{1}{t})

= \frac{d}{d t} (tan (\frac{1}{t}))

Wende die Kettenregel an:

sec^{2} (\frac{1}{t}) \frac{d}{d t} (\frac{1}{t})

= sec^{2} (\frac{1}{t}) \frac{d}{d t} (\frac{1}{t})

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

= sec^{2} (\frac{1}{t}) (- \frac{1}{t ^{2}})

Vereinfache

sec^{2} (\frac{1}{t}) (- \frac{1}{t ^{2}}) : - \frac{sec ^{2} ( \frac{1}{t} )}{t ^{2}}

= - \frac{sec ^{2} ( \frac{1}{t} )}{t ^{2}}

\frac{d}{d x} (3^{c o s (2 x)})

x \to 3 lim (\frac{10}{x ^{2}})

\int_{0}^{4} (\frac{5 x}{x ^{2} + 9}) d x

\frac{d}{d x} ((2 x + x) (x^{2} - x))

d er i v a t i v e sec^{2} (θ)