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Beliebt Rechnen >

derivative f(x)=tan(1/x)

Lösung

ableitung von

f (x) = tan (\frac{1}{x})

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of (100x/(x+y))=0

\frac{d}{d x} (\frac{100 x}{x + y}) = 0

laplacetransform x^2e^{2x}

l a pl a ce t r an s f or m x^{2} e^{2 x}

derivative of 2sec^2(2x)

\frac{d}{d x} (2 sec^{2} (2 x))

integral from 0 to pi of sin(x^2)

\int_{0}^{π} sin (x^{2}) d x

integral of cot^3(x)

\int cot^{3} (x) d x