derivative of tan^{1/x}(x)

Lösung

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

tan^{\frac{1}{x}} (x) (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

tan^{\frac{1}{x}} (x) = e^{\frac{1}{x} l n (t a n (x))}

= \frac{d}{d x} (e^{\frac{1}{x} l n (t a n (x))})

Wende die Kettenregel an:

e^{\frac{1}{x} l n (t a n (x))} \frac{d}{d x} (\frac{1}{x} ln (tan (x)))

= e^{\frac{1}{x} l n (t a n (x))} \frac{d}{d x} (\frac{1}{x} ln (tan (x)))

\frac{d}{d x} (\frac{1}{x} ln (tan (x))) = - \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x}

= e^{\frac{1}{x} l n (t a n (x))} (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

e^{\frac{1}{x} l n (t a n (x))} = tan^{\frac{1}{x}} (x)

= tan^{\frac{1}{x}} (x) (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

\int - 3 ln (x^{2} - 1) d x

\frac{d}{d x} (ln (cos (x^{2})))

\int sin^{2} (\frac{π x}{6}) d x

x \to 1 + lim (x^{\frac{2}{1 - x}})

d er i v a t i v e 4 + 7 x